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Publications of Robert Bryant    :chronological  alphabetical  by type listing:

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@article{fds325462,
   Author = {Bryant, RL and Huang, L and Mo, X},
   Title = {On Finsler surfaces of constant flag curvature with a
             Killing field},
   Journal = {Journal of Geometry and Physics},
   Volume = {116},
   Pages = {345-357},
   Year = {2017},
   Month = {June},
   url = {http://dx.doi.org/10.1016/j.geomphys.2017.02.012},
   Doi = {10.1016/j.geomphys.2017.02.012},
   Key = {fds325462}
}

@article{fds320294,
   Author = {Bryant, RL},
   Title = {On the convex Pfaff-Darboux Theorem of Ekeland and
             Nirenberg},
   Year = {2015},
   Month = {December},
   url = {http://arxiv.org/abs/1512.07100},
   Abstract = {The classical Pfaff-Darboux Theorem, which provides local
             `normal forms' for 1-forms on manifolds, has applications in
             the theory of certain economic models. However, the normal
             forms needed in these models come with an additional
             requirement of convexity, which is not provided by the
             classical proofs of the Pfaff-Darboux Theorem. (The
             appropriate notion of `convexity' is a feature of the
             economic model. In the simplest case, when the economic
             model is formulated in a domain in n-space, convexity has
             its usual meaning. In 2002, Ekeland and Nirenberg were able
             to characterize necessary and sufficient conditions for a
             given 1-form to admit a convex local normal form (and to
             show that some earlier attempts at this characterization had
             been unsuccessful). In this article, after providing some
             necessary background, I prove a strengthened and generalized
             convex Pfaff-Darboux Theorem, one that covers the case of a
             Legendrian foliation in which the notion of convexity is
             defined in terms of a torsion-free affine connection on the
             underlying manifold. (The main result in Ekeland and
             Nirenberg's paper concerns the case in which the affine
             connection is flat.)},
   Key = {fds320294}
}

@article{fds320295,
   Author = {Bryant, RL},
   Title = {On the conformal volume of 2-tori},
   Year = {2015},
   Month = {July},
   url = {http://arxiv.org/abs/1507.01485},
   Keywords = {conformal volume},
   Abstract = {This note provides a proof of a 1985 conjecture of Montiel
             and Ros about the conformal volume of tori. (This material
             is not really new; I'm making it available now because of
             requests related to recent interest in the
             conjecture.)},
   Key = {fds320295}
}

@article{fds320296,
   Author = {Bryant, RL},
   Title = {S.-S. Chern's study of almost-complex structures on the
             six-sphere},
   Year = {2014},
   Month = {May},
   url = {http://arxiv.org/abs/1405.3405},
   Keywords = {6-sphere • complex structure • exceptional
             geometry},
   Abstract = {In 2003, S.-s. Chern began a study of almost-complex
             structures on the 6-sphere, with the idea of exploiting the
             special properties of its well-known almost-complex
             structure invariant under the exceptional group $G_2$. While
             he did not solve the (currently still open) problem of
             determining whether there exists an integrable
             almost-complex structure on the 6-sphere, he did prove a
             significant identity that resolves the question for an
             interesting class of almost-complex structures on the
             6-sphere.},
   Key = {fds320296}
}

@article{fds320297,
   Author = {Bryant, RL},
   Title = {Notes on exterior differential systems},
   Year = {2014},
   Month = {May},
   url = {http://arxiv.org/abs/1405.3116},
   Keywords = {exterior differential systems • Lie theory •
             differential geometry},
   Abstract = {These are notes for a very rapid introduction to the basics
             of exterior differential systems and their connection with
             what is now known as Lie theory, together with some typical
             and not-so-typical applications to illustrate their
             use.},
   Key = {fds320297}
}

@article{fds320298,
   Author = {Bryant, RL and Eastwood, MG and Gover, AR and Neusser,
             K},
   Title = {Some differential complexes within and beyond parabolic
             geometry},
   Year = {2012},
   Month = {March},
   Abstract = {For smooth manifolds equipped with various geometric
             structures, we construct complexes that replace the de Rham
             complex in providing an alternative fine resolution of the
             sheaf of locally constant functions. In case that the
             geometric structure is that of a parabolic geometry, our
             complexes coincide with the Bernstein-Gelfand-Gelfand
             complex associated with the trivial representation. However,
             at least in the cases we discuss, our constructions are
             relatively simple and avoid most of the machinery of
             parabolic geometry. Moreover, our method extends to certain
             geometries beyond the parabolic realm.},
   Key = {fds320298}
}

@book{fds318258,
   Author = {R. Bryant and Bryant, RL and Chern, SS and Gardner, RB and Goldschmidt, HL and Griffiths, PA},
   Title = {Exterior Differential Systems},
   Pages = {475 pages},
   Publisher = {Springer},
   Year = {2011},
   Month = {December},
   ISBN = {1461397162},
   MRNUMBER = {92h:58007},
   url = {http://www.ams.org/mathscinet-getitem?mr=92h:58007},
   Abstract = {This book gives a treatment of exterior differential
             systems.},
   Key = {fds318258}
}

@article{fds216495,
   Author = {R. Bryant and Michael G. Eastwood and A. Rod. Gover and Katharina
             Neusser},
   Title = {Some differential complexes within and beyond parabolic
             geometry},
   Year = {2011},
   Month = {December},
   url = {http://arxiv.org/abs/1112.2142v2},
   Abstract = {For smooth manifolds equipped with various geometric
             structures, we construct complexes that replace the de Rham
             complex in providing an alternative fine resolution of the
             sheaf of locally constant functions. In case that the
             geometric structure is that of a parabolic geometry, our
             complexes coincide with the Bernstein- Gelfand-Gelfand
             complex associated with the trivial representation. However,
             at least in the cases we discuss, our constructions are
             relatively simple and avoid most of the machinery of
             parabolic geometry. Moreover, our method extends to certain
             geometries beyond the parabolic realm.},
   Key = {fds216495}
}

@article{fds320299,
   Author = {Bryant, R and Xu, F},
   Title = {Laplacian Flow for Closed $G_2$-Structures: Short Time
             Behavior},
   Year = {2011},
   Month = {January},
   Abstract = {We prove short time existence and uniqueness of solutions to
             the Laplacian flow for closed $G_2$ structures on a compact
             manifold $M^7$. The result was claimed in \cite{BryantG2},
             but its proof has never appeared.},
   Key = {fds320299}
}

@article{fds225242,
   Author = {R.L. Bryant and Feng Xu},
   Title = {Laplacian flow for closed G2-structures: short
             time behavior},
   Year = {2011},
   Month = {January},
   url = {http://arxiv.org/abs/1101.2004},
   Abstract = {We prove short time existence and uniqueness of solutions to
             the Laplacian flow for closed G2 structures on a compact
             manifold M7. The result was claimed in \cite{BryantG2}, but
             its proof has never appeared.},
   Key = {fds225242}
}

@article{fds243372,
   Author = {Bryant, RL},
   Title = {Nonembedding and nonextension results in special
             holonomy},
   Pages = {346-367},
   Booktitle = {The Many Facets of Geometry: A Tribute to Nigel
             Hitchin},
   Publisher = {Oxford University Press},
   Address = {Oxford},
   Editor = {Garcia-Prada, O and Bourguignon, JP and Salamon,
             S},
   Year = {2010},
   Month = {Fall},
   ISBN = {0199534926},
   MRCLASS = {53C29},
   MRNUMBER = {MR2681703},
   url = {http://dx.doi.org/10.1093/acprof:oso/9780199534920.003.0017},
   Abstract = {Constructions of metrics with special holonomy by methods of
             exterior differential systems are reviewed and the
             interpretations of these construction as `flows' on
             hypersurface geometries are considered. It is shown that
             these hypersurface 'flows' are not generally well-posed for
             smooth initial data and counterexamples to existence are
             constructed.},
   Doi = {10.1093/acprof:oso/9780199534920.003.0017},
   Key = {fds243372}
}

@article{fds243377,
   Author = {Bryant, RL},
   Title = {Commentary},
   Journal = {Bulletin of the American Mathematical Society},
   Volume = {46},
   Number = {2},
   Pages = {177-178},
   Year = {2009},
   ISSN = {0273-0979},
   url = {http://dx.doi.org/10.1090/S0273-0979-09-01248-8},
   Doi = {10.1090/S0273-0979-09-01248-8},
   Key = {fds243377}
}

@article{fds243378,
   Author = {R. Bryant and Bryant, RL and Dunajski, M and Eastwood, M},
   Title = {Metrisability of two-dimensional projective
             structures},
   Volume = {83},
   Number = {3},
   Pages = {465-499},
   Year = {2009},
   ISSN = {0022-040X},
   MRCLASS = {53},
   MRNUMBER = {MR2581355},
   url = {http://arxiv.org/abs/0801.0300v1},
   Abstract = {We carry out the programme of R. Liouville \cite{Liouville}
             to construct an explicit local obstruction to the existence
             of a Levi--Civita connection within a given projective
             structure $[\Gamma]$ on a surface. The obstruction is of
             order 5 in the components of a connection in a projective
             class. It can be expressed as a point invariant for a second
             order ODE whose integral curves are the geodesics of
             $[\Gamma]$ or as a weighted scalar projective invariant of
             the projective class. If the obstruction vanishes we find
             the sufficient conditions for the existence of a metric in
             the real analytic case. In the generic case they are
             expressed by the vanishing of two invariants of order 6 in
             the connection. In degenerate cases the sufficient
             obstruction is of order at most 8.},
   Key = {fds243378}
}

@article{fds243385,
   Author = {R. Bryant and Bryant, RL and Manno, G and Matveev, VS},
   Title = {A solution of a problem of Sophus Lie: Normal forms of
             two-dimensional metrics admitting two projective vector
             fields},
   Journal = {Mathematische Annalen},
   Volume = {340},
   Number = {2},
   Pages = {437-463},
   Year = {2008},
   Month = {Spring},
   url = {http://www.arxiv.org/abs/0705.3592},
   Abstract = {We give a complete list of normal forms for the
             two-dimensional metrics that admit a transitive Lie
             pseudogroup of geodesic-preserving transformations and we
             show that these normal forms are mutually non-isometric.
             This solves a problem posed by Sophus Lie. © 2007
             Springer-Verlag.},
   Doi = {10.1007/s00208-007-0158-3},
   Key = {fds243385}
}

@article{fds320198,
   Author = {Bryant, RL},
   Title = {Gradient Kähler Ricci solitons},
   Journal = {Asterisque},
   Volume = {321},
   Series = {Astérisque},
   Number = {321},
   Pages = {51-97},
   Booktitle = {Géométrie différentielle, physique mathématique,
             mathématiques et société. I.},
   Publisher = {Soc. Math. France},
   Year = {2008},
   Month = {Spring},
   ISBN = {978-285629-258-7},
   MRCLASS = {53C55 (53C21)},
   MRNUMBER = {2010i:53138},
   url = {http://arxiv.org/abs/math/0407453},
   Abstract = {Some observations about the local and global generality of
             gradient Kahler Ricci solitons are made, including the
             existence of a canonically associated holomorphic volume
             form and vector field, the local generality of solutions
             with a prescribed holomorphic volume form and vector field,
             and the existence of Poincaré coordinates in the case that
             the Ricci curvature is positive and the vector field has a
             fixed point. © Asterisque 321.},
   Key = {fds320198}
}

@book{fds318259,
   Author = {R. Bryant and Gu, C and Berger, M and Bryant, RL},
   Title = {Differential Geometry and Differential Equations Proceedings
             of a Symposium, held in Shanghai, June 21 - July 6,
             1985},
   Pages = {246 pages},
   Publisher = {Springer},
   Year = {2006},
   Month = {November},
   ISBN = {3540478833},
   Abstract = {The DD6 Symposium was, like its predecessors DD1 to DD5 both
             a research symposium and a summer seminar and concentrated
             on differential geometry. This volume contains a selection
             of the invited papers and some additional
             contributions.},
   Key = {fds318259}
}

@article{fds243386,
   Author = {Bryant, RL},
   Title = {On the geometry of almost complex 6-manifolds},
   Journal = {The Asian Journal of Mathematics},
   Volume = {10},
   Number = {3},
   Pages = {561-606},
   Year = {2006},
   Month = {September},
   url = {http://arxiv.org/abs/math/0508428},
   Keywords = {almost complex manifolds • quasi-integrable •
             Nijenhuis tensor},
   Abstract = {This article is mostly a writeup of two talks, the first
             given in the Besse Seminar at the Ecole Polytechnique in
             1998 and the second given at the 2000 International Congress
             on Differential Geometry in memory of Alfred Gray in Bilbao,
             Spain. It begins with a discussion of basic geometry of
             almost complex 6-manifolds. In particular, I define a 2-
             parameter family of intrinsic first-order functionals on
             almost complex structures on 6-manifolds and compute their
             Euler-Lagrange equations. It also includes a discussion of a
             natural generalization of holomorphic bundles over complex
             manifolds to the almost complex case. The general almost
             complex manifold will not admit any nontrivial bundles of
             this type, but there is a large class of nonintegrable
             almost complex manifolds for which there are such nontrivial
             bundles. For example, the standard almost complex structure
             on the 6-sphere admits such nontrivial bundles. This class
             of almost complex manifolds in dimension 6 will be referred
             to as quasi-integrable. Some of the properties of
             quasi-integrable structures (both almost complex and
             unitary) are developed and some examples are given. However,
             it turns out that quasi-integrability is not an involutive
             condition, so the full generality of these structures in
             Cartan's sense is not well-understood.},
   Key = {fds243386}
}

@article{fds318260,
   Author = {BRYANT, RL},
   Title = {Conformal geometry and 3-plane fields on
             6-manifolds},
   Volume = {1502 (Developments of Cartan Geometry an},
   Series = {RIMS Symposium Proceedings},
   Pages = {1-15},
   Booktitle = {Developments of Cartan Geometry and Related Mathematical
             Problems},
   Publisher = {Kyoto University},
   Year = {2006},
   Month = {July},
   url = {http://arxiv.org/abs/math/0511110},
   Keywords = {differential invariants},
   Abstract = {The purpose of this note is to provide yet another example
             of the link between certain conformal geometries and
             ordinary differential equations, along the lines of the
             examples discussed by Nurowski in math.DG/0406400. In this
             particular case, I consider the equivalence problem for
             3-plane fields D on 6-manifolds M that satisfy the
             nondegeneracy condition that D+[D,D]=TM I give a solution of
             the equivalence problem for such D (as Tanaka has
             previously), showing that it defines a so(4,3)- valued
             Cartan connection on a principal right H-bundle over M where
             H is the subgroup of SO(4,3) that stabilizes a null 3-plane
             in R^{4,3}. Along the way, I observe that there is
             associated to each such D a canonical conformal structure of
             split type on M, one that depends on two derivatives of the
             plane field D. I show how the primary curvature tensor of
             the Cartan connection associated to the equivalence problem
             for D can be interpreted as the Weyl curvature of the
             associated conformal structure and, moreover, show that the
             split conformal structures in dimension 6 that arise in this
             fashion are exactly the ones whose so(4,4)-valued Cartan
             connection admits a reduction to a spin(4,3)-connection. I
             also discuss how this case has features that are analogous
             to those of Nurowski's examples.},
   Key = {fds318260}
}

@article{fds243387,
   Author = {Bryant, RL},
   Title = {SO(n)-invariant special Lagrangian submanifolds of C^{n+1}
             with fixed loci},
   Journal = {Chinese Annals of Mathematics, Series B},
   Volume = {27},
   Number = {1},
   Pages = {95-112},
   Year = {2006},
   Month = {January},
   MRNUMBER = {MR2209954},
   url = {http://arxiv.org/abs/math/0402201},
   Keywords = {calibrations, special Lagrangian submanifolds},
   Abstract = {Let SO(n) act in the standard way on C^n and extend this
             action in the usual way to C^{n+1}. It is shown that
             nonsingular special Lagrangian submanifold L in C^{n+1} that
             is invariant under this SO(n)-action intersects the fixed
             line C in a nonsingular real-analytic arc A (that may be
             empty). If n>2, then A has no compact component. Conversely,
             an embedded, noncompact nonsingular real-analytic arc A in C
             lies in an embedded nonsingular special Lagrangian
             submanifold that is SO(n)-invariant. The same existence
             result holds for compact A if n=2. If A is connected, there
             exist n distinct nonsingular SO(n)- invariant special
             Lagrangian extensions of A such that any embedded
             nonsingular SO(n)-invariant special Lagrangian extension of
             A agrees with one of these n extensions in some open
             neighborhood of A. The method employed is an analysis of a
             singular nonlinear PDE and ultimately calls on the work of
             Gerard and Tahara to prove the existence of the
             extension.},
   Key = {fds243387}
}

@article{fds318261,
   Author = {Bryant, R and Freed, D},
   Title = {Shiing-Shen Chern - Obituary},
   Journal = {Physics today},
   Volume = {59},
   Number = {1},
   Pages = {70-72},
   Year = {2006},
   Month = {January},
   url = {http://dx.doi.org/10.1063/1.2180187},
   Doi = {10.1063/1.2180187},
   Key = {fds318261}
}

@article{fds318262,
   Author = {Bryant, RL},
   Title = {Second order families of special Lagrangian
             3-folds},
   Journal = {Perspectives in Riemannian Geometry, CRM Proceedings and
             Lecture Notes, edited by Vestislav Apostolov, Andrew Dancer,
             Nigel Hitchin, and McKenzie Wang, vol. 40 (2006), American
             Mathematical Society},
   Volume = {40},
   Series = {CRM Proceedings and Lecture Notes},
   Pages = {63-98},
   Booktitle = {Perspectives in Riemannian Geometry},
   Publisher = {American Mathematical Society},
   Editor = {Vestislav Apostolov and Andrew Dancer and Nigel Hitchin and McKenzie Wang},
   Year = {2006},
   ISBN = {0-8218-3852-0},
   url = {http://arxiv.org/abs/math/0007128},
   Abstract = {A second order family of special Lagrangian submanifolds of
             complex m-space is a family characterized by the
             satisfaction of a set of pointwise conditions on the second
             fundamental form. For example, the set of ruled special
             Lagrangian submanifolds of complex 3-space is characterized
             by a single algebraic equation on the second fundamental
             form. While the `generic' set of such conditions turns out
             to be incompatible, i.e., there are no special Lagrangian
             submanifolds that satisfy them, there are many interesting
             sets of conditions for which the corresponding family is
             unexpectedly large. In some cases, these geometrically
             defined families can be described explicitly, leading to new
             examples of special Lagrangian submanifolds. In other cases,
             these conditions characterize already known families in a
             new way. For example, the examples of Lawlor-Harvey
             constructed for the solution of the angle conjecture and
             recently generalized by Joyce turn out to be a natural and
             easily described second order family.},
   Key = {fds318262}
}

@article{fds318263,
   Author = {Bryant, RL},
   Title = {Geometry of manifolds with special holonomy: "100 years of
             holonomy"},
   Journal = {Contemporary Mathematics},
   Volume = {395},
   Series = {Contemporary Mathematics},
   Pages = {29-38},
   Booktitle = {150 years of mathematics at Washington University in St.
             Louis},
   Publisher = {AMS},
   Year = {2006},
   ISBN = {0-8218-3603-X},
   MRNUMBER = {MR2206889},
   url = {http://www.ams.org/mathscinet-getitem?mr=2206889},
   Keywords = {53C29 (70F25)},
   Key = {fds318263}
}

@article{fds318264,
   Author = {Bryant, RL},
   Title = {Geodesically reversible Finsler 2-spheres of constant
             curvature},
   Volume = {11},
   Series = {Nankai Tracts in Mathematics},
   Pages = {95-111},
   Booktitle = {Inspired by S. S. Chern---A Memorial Volume in Honor of a
             Great Mathematician},
   Publisher = {World Scientific Publishers},
   Editor = {Griffiths, PA},
   Year = {2006},
   Month = {Winter},
   url = {http://arxiv.org/abs/math/0407514},
   Abstract = {A Finsler space is said to be geodesically reversible if
             each oriented geodesic can be reparametrized as a geodesic
             with the reverse orientation. A reversible Finsler space is
             geodesically reversible, but the converse need not be true.
             In this note, building on recent work of LeBrun and Mason,
             it is shown that a geodesically reversible Finsler metric of
             constant flag curvature on the 2-sphere is necessarily
             projectively flat. As a corollary, using a previous result
             of the author, it is shown that a reversible Finsler metric
             of constant flag curvature on the 2-sphere is necessarily a
             Riemannian metric of constant Gauss curvature, thus settling
             a long-standing problem in Finsler geometry.},
   Key = {fds318264}
}

@article{fds318265,
   Author = {Bryant, RL},
   Title = {Some remarks on G_2-structures},
   Pages = {75-109},
   Booktitle = {Proceedings of Gökova Geometry-Topology Conference
             2005},
   Publisher = {International Press},
   Editor = {Akbulut, S and Onder, T and Stern, R},
   Year = {2006},
   ISBN = {1-57146-152-3},
   url = {http://arxiv.org/abs/math/0305124},
   Abstract = {This article consists of some loosely related remarks about
             the geometry of G_2-structures on 7-manifolds and is partly
             based on old unpublished joint work with two other people:
             F. Reese Harvey and Steven Altschuler. Much of this work has
             since been subsumed in the work of Hitchin
             \cite{MR02m:53070} and Joyce \cite{MR01k:53093}. I am making
             it available now mainly because of interest expressed by
             others in seeing these results written up since they do not
             seem to have all made it into the literature. A formula is
             derived for the scalar curvature and Ricci curvature of a
             G_2-structure in terms of its torsion. When the fundamental
             3-form of the G_2-structure is closed, this formula implies,
             in particular, that the scalar curvature of the underlying
             metric is nonpositive and vanishes if and only if the
             structure is torsion-free. This version contains some new
             results on the pinching of Ricci curvature for metrics
             associated to closed G_2-structures. Some formulae are
             derived for closed solutions of the Laplacian flow that
             specify how various related quantities, such as the torsion
             and the metric, evolve with the flow. These may be useful in
             studying convergence or long-time existence for given
             initial data.},
   Key = {fds318265}
}

@article{fds318266,
   Author = {Bryant, R},
   Title = {Holonomy and Special Geometries},
   Series = {Conference Proceedings and Lecture Notes in Geometry and
             Topology},
   Pages = {71-90},
   Booktitle = {Dirac Operators: Yesterday and Today},
   Publisher = {International Press},
   Editor = {Bourguinon, JP and Branson, T and Chamseddine, A and Hijazi, O and Stanton, R},
   Year = {2005},
   ISBN = {1-57146-175-2},
   MRNUMBER = {MR2205367},
   url = {http://www.ams.org/mathscinet-getitem?mr=2205367},
   Key = {fds318266}
}

@book{fds318267,
   Author = {R. Bryant and David Bao and S.-S. Chern and Zhongmin Shen},
   Title = {A Sampler of Riemann-Finsler Geometry},
   Volume = {50},
   Series = {Mathematical Sciences Research Institute
             Publications},
   Pages = {363 pages},
   Publisher = {Cambridge University Press},
   Editor = {Bao, D and Bryant, RL and Chern, S-S and Shen, Z},
   Year = {2004},
   Month = {November},
   ISBN = {0521831814},
   MRNUMBER = {MR2132655(2005j:53003)},
   url = {http://www.ams.org/mathscinet-getitem?mr=2132655},
   Abstract = {These expository accounts treat issues in Finsler geometry
             related to volume, geodesics, curvature and mathematical
             biology, with instructive examples.},
   Key = {fds318267}
}

@article{fds320300,
   Author = {Bryant, RL},
   Title = {Real hypersurfaces in unimodular complex
             surfaces},
   Year = {2004},
   Month = {July},
   url = {http://arxiv.org/abs/math/0407472},
   Abstract = {A unimodular complex surface is a complex 2-manifold X
             endowed with a holomorphic volume form. A strictly
             pseudoconvex real hypersurface M in X inherits not only a
             CR-structure but a canonical coframing as well. In this
             article, this canonical coframing on M is defined, its
             invariants are discussed and interpreted geometrically, and
             its basic properties are studied. A natural evolution
             equation for strictly pseudoconvex real hypersurfaces in
             unimodular complex surfaces is defined, some of its
             properties are discussed, and several examples are computed.
             The locally homogeneous examples are determined and used to
             illustrate various features of the geometry of the induced
             structure on the hypersurface.},
   Key = {fds320300}
}

@article{fds243379,
   Author = {R. Bryant and Bryant, R and Edelsbrunner, H and Koehl, P and Levitt,
             M},
   Title = {The area derivative of a space-filling diagram},
   Journal = {Discrete and Computanional Geometry},
   Volume = {32},
   Number = {3},
   Pages = {293-308},
   Year = {2004},
   MRNUMBER = {2005k:92077},
   url = {http://dx.doi.org/10.1007/s00454-004-1099-1},
   Abstract = {The motion of a biomolecule greatly depends on the engulfing
             solution, which is mostly water. Instead of representing
             individual water molecules, it is desirable to develop
             implicit solvent models that nevertheless accurately
             represent the contribution of the solvent interaction to the
             motion. In such models, hydrophobicity is expressed as a
             weighted sum of atomic surface areas. The derivatives of
             these weighted areas contribute to the force that drives the
             motion. In this paper we give formulas for the weighted and
             unweighted area derivatives of a molecule modeled as a
             space-filling diagram made up of balls in motion. Other than
             the radii and the centers of the balls, the formulas are
             given in terms of the sizes of circular arcs of the boundary
             and edges of the power diagram. We also give
             inclusion-exclusion formulas for these sizes.},
   Doi = {10.1007/s00454-004-1099-1},
   Key = {fds243379}
}

@book{fds318268,
   Author = {R. Bryant and Bryant, RL and Griffiths, PA and Grossman, DA},
   Title = {Exterior Differential Systems and Euler-Lagrange Partial
             Differential Equations},
   Series = {Chicago Lectures in Mathematics},
   Pages = {213 pages},
   Publisher = {University of Chicago Press},
   Year = {2003},
   Month = {July},
   ISBN = {0226077934},
   MRNUMBER = {MR1985469},
   url = {http://arxiv.org/abs/math/0207039},
   Abstract = {We use methods from exterior differential systems (EDS) to
             develop a geometric theory of scalar, first-order Lagrangian
             functionals and their associated Euler-Lagrange PDEs,
             subject to contact transformations. The first chapter
             contains an introduction of the classical Poincare-Cartan
             form in the context of EDS, followed by proofs of classical
             results, including a solution to the relevant inverse
             problem, Noether's theorem on symmetries and conservation
             laws, and several aspects of minimal hypersurfaces. In the
             second chapter, the equivalence problem for Poincare-Cartan
             forms is solved, giving the differential invariants of such
             a form, identifying associated geometric structures
             (including a family of affine hypersurfaces), and exhibiting
             certain "special" Euler-Lagrange equations characterized by
             their invariants. In the third chapter, we discuss a
             collection of Poincare-Cartan forms having a naturally
             associated conformal geometry, and exhibit the conservation
             laws for non-linear Poisson and wave equations that result
             from this. The fourth and final chapter briefly discusses
             additional PDE topics from this viewpoint--Euler-Lagrange
             PDE systems, higher order Lagrangians and conservation laws,
             identification of local minima for Lagrangian functionals,
             and Backlund transformations. No previous knowledge of
             exterior differential systems or of the calculus of
             variations is assumed.},
   Key = {fds318268}
}

@book{fds43013,
   Title = {Selected works of Phillip A. Griffiths with commentary. Part
             4. Differential systems.},
   Publisher = {American Mathematical Society, Providence, RI; International
             Press, Somerville, MA},
   Editor = {R. L. Bryant and David R. Morrison},
   Year = {2003},
   MRNUMBER = {2005e:01025d},
   url = {http://www.ams.org/mathscinet-getitem?mr=2005e:01025d},
   Key = {fds43013}
}

@article{fds10364,
   Author = {R. Bryant},
   Title = {Levi-flat minimal hypersurfaces in two-dimensional complex
             space forms},
   Volume = {37},
   Series = {Adv. Stud. Pure Math.},
   Pages = {1--44},
   Booktitle = {Lie groups, geometric structures and differential
             equations---one hundred years after Sophus Lie (Kyoto/Nara,
             1999)},
   Publisher = {Math. Soc. Japan},
   Year = {2002},
   MRNUMBER = {MR1980895},
   url = {http://arxiv.org/abs/math/9909159},
   Abstract = {The purpose of this article is to classify the real
             hypersurfaces in complex space forms of dimension 2 that are
             both Levi-flat and minimal. The main results are as follows:
             When the curvature of the complex space form is nonzero,
             there is a 1-parameter family of such hypersurfaces.
             Specifically, for each one-parameter subgroup of the
             isometry group of the complex space form, there is an
             essentially unique example that is invariant under this
             one-parameter subgroup. On the other hand, when the
             curvature of the space form is zero, i.e., when the space
             form is complex 2-space with its standard flat metric, there
             is an additional `exceptional' example that has no
             continuous symmetries but is invariant under a lattice of
             translations. Up to isometry and homothety, this is the
             unique example with no continuous symmetries.},
   Key = {fds10364}
}

@article{fds243380,
   Author = {Bryant, RL},
   Title = {Some remarks on Finsler manifolds with constant flag
             curvature},
   Journal = {Houston Journal of Mathematics},
   Volume = {28},
   Number = {2},
   Pages = {221-262},
   Year = {2002},
   MRNUMBER = {2003h:53102},
   url = {HJM},
   Abstract = {This article is an exposition of four loosely related
             remarks on the geometry of Finsler manifolds with constant
             positive flag curvature. The first remark is that there is a
             canonical Kahler structure on the space of geodesics of such
             a manifold. The second remark is that there is a natural way
             to construct a (not necessarily complete) Finsler n-manifold
             of constant positive flag curvature out of a hypersurface in
             suitably general position in complex projective n-space. The
             third remark is that there is a description of the Finsler
             metrics of constant curvature on the 2-sphere in terms of a
             Riemannian metric and 1-form on the space of its geodesics.
             In particular, this allows one to use any (Riemannian) Zoll
             metric of positive Gauss curvature on the 2-sphere to
             construct a global Finsler metric of constant positive
             curvature on the 2-sphere. The fourth remark concerns the
             generality of the space of (local) Finsler metrics of
             constant positive flag curvature in dimension n+1>2 . It is
             shown that such metrics depend on n(n+1) arbitrary functions
             of n+1 variables and that such metrics naturally correspond
             to certain torsion- free S^1 x GL(n,R)-structures on
             2n-manifolds. As a by- product, it is found that these
             groups do occur as the holonomy of torsion-free affine
             connections in dimension 2n, a hitherto unsuspected
             phenomenon. },
   Key = {fds243380}
}

@book{fds320301,
   Author = {Bryant, RL},
   Title = {Rigidity and quasi-rigidity of extremal cycles in Hermitian
             symmetric spaces},
   Year = {2001},
   Month = {March},
   url = {http://arxiv.org/abs/math/0006186},
   Abstract = {I use local differential geometric techniques to prove that
             the algebraic cycles in certain extremal homology classes in
             Hermitian symmetric spaces are either rigid (i.e.,
             deformable only by ambient motions) or quasi-rigid (roughly
             speaking, foliated by rigid subvarieties in a nontrivial
             way). These rigidity results have a number of applications:
             First, they prove that many subvarieties in Grassmannians
             and other Hermitian symmetric spaces cannot be smoothed
             (i.e., are not homologous to a smooth subvariety). Second,
             they provide characterizations of holomorphic bundles over
             compact Kahler manifolds that are generated by their global
             sections but that have certain polynomials in their Chern
             classes vanish (for example, c_2 = 0, c_1c_2 - c_3 = 0, c_3
             = 0, etc.).},
   Key = {fds320301}
}

@article{MR2002i:53010,
   Author = {Bryant, RL},
   Title = {On surfaces with prescribed shape operator},
   Journal = {Results Math. 40 (2001), no. 1-4, 88--121},
   Volume = {40},
   Number = {1--4},
   Pages = {88-121},
   Year = {2001},
   MRNUMBER = {2002i:53010},
   url = {http://arxiv.org/abs/math/0107083},
   Abstract = {The problem of immersing a simply connected surface with a
             prescribed shape operator is discussed. From classical and
             more recent work, it is known that, aside from some special
             degenerate cases, such as when the shape operator can be
             realized by a surface with one family of principal curves
             being geodesic, the space of such realizations is a convex
             set in an affine space of dimension at most 3. The cases
             where this maximum dimension of realizability is achieved
             have been classified and it is known that there are two such
             families of shape operators, one depending essentially on
             three arbitrary functions of one variable (called Type I in
             this article) and another depending essentially on two
             arbitrary functions of one variable (called Type II in this
             article). In this article, these classification results are
             rederived, with an emphasis on explicit computability of the
             space of solutions. It is shown that, for operators of
             either type, their realizations by immersions can be
             computed by quadrature. Moreover, explicit normal forms for
             each can be computed by quadrature together with, in the
             case of Type I, by solving a single linear second order ODE
             in one variable. (Even this last step can be avoided in most
             Type I cases.) The space of realizations is discussed in
             each case, along with some of their remarkable geometric
             properties. Several explicit examples are constructed
             (mostly already in the literature) and used to illustrate
             various features of the problem.},
   Key = {MR2002i:53010}
}

@article{fds243382,
   Author = {Bryant, RL},
   Title = {Bochner-Kähler metrics},
   Journal = {Journal of the AMS},
   Volume = {14},
   Number = {3},
   Pages = {623-715},
   Year = {2001},
   MRNUMBER = {2002i:53096},
   url = {http://arxiv.org/abs/math/0003099},
   Abstract = {A Kahler metric is said to be Bochner-Kahler if its Bochner
             curvature vanishes. This is a nontrivial condition when the
             complex dimension of the underlying manifold is at least 2.
             In this article it will be shown that, in a certain well-
             defined sense, the space of Bochner-Kahler metrics in
             complex dimension n has real dimension n+1 and a recipe for
             an explicit formula for any Bochner-Kahler metric is given.
             It is shown that any Bochner-Kahler metric in complex
             dimension n has local (real) cohomogeneity at most~n. The
             Bochner-Kahler metrics that can be `analytically continued'
             to a complete metric, free of singularities, are identified.
             In particular, it is shown that the only compact Bochner-
             Kahler manifolds are the discrete quotients of the known
             symmetric examples. However, there are compact Bochner-
             Kahler orbifolds that are not locally symmetric. In fact,
             every weighted projective space carries a Bochner-Kahler
             metric. The fundamental technique is to construct a
             canonical infinitesimal torus action on a Bochner-Kahler
             metric whose associated momentum mapping has the orbits of
             its symmetry pseudo-groupoid as fibers.},
   Key = {fds243382}
}

@article{fds243383,
   Author = {Bryant, RL},
   Title = {Recent advances in the theory of holonomy},
   Journal = {Asterisque},
   Volume = {266},
   Number = {5},
   Pages = {351-374},
   Publisher = {Centre National de la Recherche Scientifique},
   Year = {2000},
   MRNUMBER = {2001h:53067},
   url = {http://www.dmi.ens.fr/bourbaki/Prog_juin99.html},
   Key = {fds243383}
}

@article{fds243384,
   Author = {Bryant, RL},
   Title = {Harmonic morphisms with fibers of dimension
             one},
   Journal = {Communications in Analysis and Geometry},
   Volume = {8},
   Number = {2},
   Pages = {219-265},
   Year = {2000},
   MRNUMBER = {2001i:53101},
   url = {http://arxiv.org/abs/dg-ga/9701002},
   Abstract = {I prove three classification results about harmonic
             morphisms whose fibers have dimension one. All are valid
             when the domain is at least of dimension 4. (The character
             of this overdetermined problem is very different when the
             dimension of the domain is 3 or less.) The first result is a
             local classification for such harmonic morphisms with
             specified target metric, the second is a finiteness theorem
             for such harmonic morphisms with specified domain metric,
             and the third is a complete classification of such harmonic
             morphisms when the domain is a space form of constant
             sectional curvature. The methods used are exterior
             differential systems and the moving frame. The basic results
             are local, but, because of the rigidity of the solutions,
             they allow a complete global classification.},
   Key = {fds243384}
}

@article{fds243409,
   Author = {Bryant, RL},
   Title = {Calibrated Embeddings in the Special Lagrangian and
             Coassociative Cases},
   Journal = {Annals of Global Analysis and Geometry},
   Volume = {18},
   Number = {3-4},
   Pages = {405-435},
   Year = {2000},
   MRNUMBER = {2002j:53063},
   url = {http://arxiv.org/abs/math/9912246},
   Abstract = {Every closed, oriented, real analytic Riemannian 3-manifold
             can be isometrically embedded as a special Lagrangian
             submanifold of a Calabi-Yau 3-fold, even as the real locus
             of an antiholomorphic, isometric involution. Every closed,
             oriented, real analytic Riemannian 4-manifold whose bundle
             of self-dual 2-forms is trivial can be isometrically
             embedded as a coassociative submanifold in a G2-manifold,
             even as the fixed locus of an anti-G2 involution. These
             results, when coupled with McLean's analysis of the moduli
             spaces of such calibrated sub-manifolds, yield a plentiful
             supply of examples of compact calibrated submanifolds with
             nontrivial deformation spaces.},
   Key = {fds243409}
}

@article{fds318269,
   Author = {Bryant, R},
   Title = {Élie Cartan and geometric duality},
   Journal = {Journées Élie Cartan 1998 et 1999},
   Volume = {16},
   Pages = {5-20},
   Booktitle = {Journées Élie Cartan 1998 et 1999},
   Publisher = {Institut Élie Cartan},
   Year = {2000},
   url = {http://www.math.duke.edu/~bryant/Cartan.pdf},
   Key = {fds318269}
}

@article{fds318270,
   Author = {Bryant, RL},
   Title = {Pseudo-Riemannian metrics with parallel spinor fields and
             vanishing Ricci tensor},
   Volume = {4},
   Series = {Séminaires & Congrès},
   Pages = {53-94},
   Booktitle = {Global analysis and harmonic analysis (Marseille-Luminy,
             1999)},
   Publisher = {Société Mathématique de France},
   Editor = {Bourguinon, JP and Branson, T and Hijazi, O},
   Year = {2000},
   ISBN = {2-85629-094-9},
   MRNUMBER = {2002h:53082},
   url = {http://arxiv.org/abs/math/0004073},
   Abstract = {I discuss geometry and normal forms for pseudo-Riemannian
             metrics with parallel spinor fields in some interesting
             dimensions. I also discuss the interaction of these
             conditions for parallel spinor fields with the condition
             that the Ricci tensor vanish (which, for pseudo-Riemannian
             manifolds, is not an automatic consequence of the existence
             of a nontrivial parallel spinor field).},
   Key = {fds318270}
}

@article{fds243402,
   Author = {Bryant, RL},
   Title = {Some examples of special Lagrangian tori},
   Journal = {Adv. Theor. Math. Phys.},
   Volume = {3},
   Number = {1},
   Pages = {83-90},
   Year = {1999},
   MRNUMBER = {2000f:32033},
   url = {http://arxiv.org/abs/math/9902076},
   Abstract = {A short paper giving some examples of smooth hypersurfaces M
             of degree n+1 in complex projective n-space that are defined
             by real polynomial equations and whose real slice contains a
             component diffeomorphic to an n-1 torus, which is then
             special Lagrangian with respect to the Calabi-Yau metric on
             M.},
   Key = {fds243402}
}

@article{fds243408,
   Author = {R. Bryant and Sharpe, E and Bryant, RL},
   Title = {D-branes and Spin^c-structures},
   Journal = {Physics Letters, Section B: Nuclear, Elementary Particle and
             High-Energy Physics},
   Volume = {450},
   Number = {4},
   Pages = {353-357},
   Year = {1999},
   MRNUMBER = {2000c:53054},
   url = {http://arxiv.org/abs/hep-th/98l2084},
   Abstract = {It was recently pointed out by E. Witten that for a D-brane
             to consistently wrap a submanifold of some manifold, the
             normal bundle must admit a Spin^c structure. We examine this
             constraint in the case of type II string compactifications
             with vanishing cosmological constant and argue that, in all
             such cases, the normal bundle to a sypersymmetric cycle is
             automatically Spin^c.},
   Key = {fds243408}
}

@article{fds10011,
   Author = {Russell, Thomas and Farris, Frank},
   Title = {Integrability, Gorman systems, and the Lie bracket structure
             of the real line (with an appendix by –––)},
   Journal = {J. Math. Econom.},
   Volume = {29},
   Number = {2},
   Pages = {183–209},
   Year = {1998},
   MRNUMBER = {99f:90029},
   url = {http://www.ams.org/mathscinet-getitem?mr=99f:90029},
   Key = {fds10011}
}

@article{fds243403,
   Author = {Bryant, RL},
   Title = {Projectively flat Finsler 2-spheres of constant
             curvature},
   Journal = {Selecta Math. (N.S.)},
   Volume = {3},
   Number = {2},
   Pages = {161-203},
   Year = {1997},
   MRNUMBER = {98i:53101},
   url = {http://arxiv.org/abs/dg-ga/9611010},
   Key = {fds243403}
}

@article{fds8915,
   Title = {Finsler structures on the 2-sphere satisfying
             K=1},
   Volume = {196},
   Series = {Contemporary Mathematics},
   Pages = {27–41},
   Booktitle = {Finsler geometry (Seattle, WA, 1995)},
   Publisher = {Amer. Math. Soc., Providence, RI},
   Editor = {David Bao and Shiing-shen Chern and Zhongmin
             Shen},
   Year = {1996},
   MRNUMBER = {97e:53128},
   url = {http://www.math.duke.edu/preprints/95-11.dvi},
   Key = {fds8915}
}

@article{fds318271,
   Author = {Bryant, RL},
   Title = {On extremals with prescribed Lagrangian densities},
   Volume = {36},
   Series = {Symposia Mathematica},
   Pages = {86-111},
   Booktitle = {Manifolds and geometry (Pisa, 1993)},
   Publisher = {Cambridge University Press},
   Editor = {Bartolomeis, P and Tricerri, F and Vesentini, E},
   Year = {1996},
   ISBN = {0-521-56216-3},
   MRNUMBER = {99a:58043},
   url = {http://arxiv.org/abs/dg-ga/9406001},
   Abstract = {Consider two manifolds~$M^m$ and $N^n$ and a first-order
             Lagrangian $L(u)$ for mappings $u:M\to N$, i.e., $L$ is an
             expression involving $u$ and its first derivatives whose
             value is an $m$-form (or more generally, an $m$-density)
             on~$M$. One is usually interested in describing the extrema
             of the functional $\Cal L(u) = \int_M L(u)$, and these are
             characterized locally as the solutions of the Euler-Lagrange
             equation~$E_L(u)=0$ associated to~$L$. In this note I will
             discuss three problems which can be understood as trying to
             determine how many solutions exist to the Euler-Lagrange
             equation which also satisfy $L(u) = \Phi$, where $\Phi$ is a
             specified $m$-form or $m$-density on~$M$. The first problem,
             which is solved completely, is to determine when two minimal
             graphs over a domain in the plane can induce the same area
             form without merely differing by a vertical translation or
             reflection. The second problem, described more fully below,
             arose in Professor Calabi's study of extremal isosystolic
             metrics on surfaces. The third problem, also solved
             completely, is to determine the (local) harmonic maps
             between spheres which have constant energy
             density.},
   Key = {fds318271}
}

@article{fds318272,
   Author = {Bryant, R},
   Title = {Classical, exceptional, and exotic holonomies: a status
             report},
   Volume = {1},
   Series = {Sémin. Congr.},
   Pages = {93-165},
   Booktitle = {Actes de la Table Ronde de Géométrie Différentielle},
   Publisher = {Société Mathématique de France},
   Editor = {Besse, A},
   Year = {1996},
   ISBN = {2-85629-047-7},
   MRNUMBER = {98c:53037},
   url = {http://www.math.duke.edu/preprints/95-10.dvi},
   Abstract = {A survey paper on the status of the holonomy problem as of
             1995.},
   Key = {fds318272}
}

@article{fds243407,
   Author = {R. Bryant and Bryant, RL and Griffiths, PA},
   Title = {Characteristic cohomology of differential systems. I.
             General theory},
   Journal = {The Journal of the American Mathematical
             Society},
   Volume = {8},
   Number = {3},
   Pages = {507-507},
   Year = {1995},
   Month = {September},
   MRNUMBER = {96c:58183},
   url = {http://www.math.duke.edu/preprints/93-01.dvi},
   Doi = {10.1090/S0894-0347-1995-1311820-X},
   Key = {fds243407}
}

@article{fds243404,
   Author = {R. Bryant and Griffiths, PA and Hsu, L and Bryant, RL},
   Title = {Hyperbolic exterior differential systems and their
             conservation laws, Part II},
   Journal = {Selecta Math. (N.S.)},
   Volume = {1},
   Number = {2},
   Pages = {265-323},
   Year = {1995},
   MRNUMBER = {97d:580009},
   url = {http://www.math.duke.edu/preprints/94-13.dvi},
   Key = {fds243404}
}

@article{fds243405,
   Author = {R. Bryant and Griffiths, PA and Hsu, L and Bryant, RL},
   Title = {Hyperbolic exterior differential systems and their
             conservation laws, Part I},
   Journal = {Selecta Math. (N.S.)},
   Volume = {1},
   Number = {1},
   Pages = {21-112},
   Year = {1995},
   MRNUMBER = {97d:580008},
   url = {http://www.math.duke.edu/preprints/94-13.dvi},
   Key = {fds243405}
}

@article{fds243406,
   Author = {R. Bryant and Bryant, RL and Griffiths, PA},
   Title = {Characteristic cohomology of differential systems, II:
             Conservation laws for a class of parabolic
             equations},
   Journal = {Duke Math. Journal},
   Volume = {78},
   Number = {3},
   Pages = {531-676},
   Year = {1995},
   MRNUMBER = {96d:58158},
   url = {http://www.math.duke.edu/preprints/93-02.dvi},
   Key = {fds243406}
}

@article{fds318273,
   Author = {R. Bryant and BRYANT, R and GRIFFITHS, P and HSU, L},
   Title = {Toward a geometry of differential equations},
   Journal = {GEOMETRY, TOPOLOGY & PHYSICS},
   Volume = {4},
   Series = {Conf. Proc. Lecture Notes Geom. Topology},
   Pages = {1-76},
   Booktitle = {Geometry, Topology, & Physics},
   Publisher = {Internat. Press, Cambridge, MA},
   Editor = {S.-T. Yau},
   Year = {1995},
   ISBN = {1-57146-024-1},
   MRNUMBER = {97b:58005},
   url = {http://www.math.duke.edu/preprints/94-12.dvi},
   Key = {fds318273}
}

@article{fds318274,
   Author = {R. Bryant and Bryant, R and Gardner, RB},
   Title = {Control Structures},
   Volume = {12},
   Series = {Banach Center Publications},
   Pages = {111-121},
   Booktitle = {Geometry in nonlinear control and differential inclusions
             (Warsaw, 1993)},
   Publisher = {Polish Academy of Sciences},
   Editor = {Jakubczyk, B and Respondek, W and Rzezuchowski,
             T},
   Year = {1995},
   MRNUMBER = {96h:93024},
   url = {http://www.math.duke.edu/preprints/94-11.dvi},
   Key = {fds318274}
}

@article{fds318275,
   Author = {Bryant, R},
   Title = {An introduction to Lie groups and symplectic
             geometry},
   Volume = {1},
   Series = {IAS/Park City Mathematics},
   Pages = {5-181},
   Booktitle = {Geometry and quantum field theory (Park City, UT,
             1991)},
   Publisher = {American Mathematical Society},
   Editor = {Freed, D and Uhlenbeck, K},
   Year = {1995},
   ISBN = {0-8218-0400-6},
   MRNUMBER = {96i:58002},
   url = {http://www.ams.org/mathscinet-getitem?mr=96i:58002},
   Abstract = {A series of lectures on Lie groups and symplectic geometry,
             aimed at the beginning graduate student level.},
   Key = {fds318275}
}

@article{fds243401,
   Author = {R. Bryant and Bryant, RL and Hsu, L},
   Title = {Rigidity of integral curves of rank 2 distributions},
   Journal = {Inventiones mathematicae},
   Volume = {114},
   Number = {1},
   Pages = {435-461},
   Year = {1993},
   ISSN = {0020-9910},
   MRNUMBER = {94j:58003},
   url = {http://www.math.duke.edu/~bryant/Rigid.dvi},
   Doi = {10.1007/BF01232676},
   Key = {fds243401}
}

@article{fds243400,
   Author = {Bryant, RL},
   Title = {Some remarks on the geometry of austere manifolds},
   Journal = {Bol. Soc. Brasil. Mat. (N.S.)},
   Volume = {21},
   Number = {2},
   Pages = {133-157},
   Year = {1991},
   MRNUMBER = {92k:53112},
   url = {http://www.math.duke.edu/preprints/90-03.dvi},
   Key = {fds243400}
}

@article{fds318276,
   Author = {Bryant, R},
   Title = {Two exotic holonomies in dimension four, path geometries,
             and twistor theory},
   Volume = {53},
   Series = {Proc. Sympos. Pure Math.},
   Pages = {33-88},
   Booktitle = {Complex geometry and Lie theory (Sundance, UT,
             1989)},
   Publisher = {American Mathematical Society},
   Editor = {Carlson, J and Clemens, H and Morrison, D},
   Year = {1991},
   ISBN = {0-8218-1492-3},
   MRNUMBER = {93e:53030},
   url = {http://www.math.duke.edu/~bryant/ExoticHol.dvi},
   Key = {fds318276}
}

@article{fds243398,
   Author = {R. Bryant and Harvey, FR and Bryant, RL},
   Title = {Submanifolds in hyper-Kähler geometry},
   Journal = {J. Amer. Math. Soc.},
   Volume = {2},
   Number = {1},
   Pages = {1-31},
   Year = {1989},
   MRNUMBER = {89m:53090},
   url = {http://www.ams.org/mathscinet-getitem?mr=89m:53090},
   Key = {fds243398}
}

@article{fds243399,
   Author = {R. Bryant and Salamon, S and Bryant, RL},
   Title = {On the construction of some complete metrics with
             exceptional holonomy},
   Journal = {Duke Math. J.},
   Volume = {58},
   Number = {3},
   Pages = {829-850},
   Year = {1989},
   MRNUMBER = {90i:53055},
   url = {http://www.ams.org/mathscinet-getitem?mr=90i:53055},
   Key = {fds243399}
}

@article{fds318277,
   Author = {Bryant, R},
   Title = {Surfaces in conformal geometry},
   Volume = {48},
   Series = {Proc. Sympos. Pure Math.},
   Pages = {227-240},
   Booktitle = {The mathematical heritage of Hermann Weyl (Durham, NC,
             1987)},
   Publisher = {American Mathematical Society},
   Editor = {Wells, RO},
   Year = {1988},
   ISBN = {0-8218-1482-6},
   MRNUMBER = {89m:53102},
   url = {http://www.ams.org/mathscinet-getitem?mr=89m:53102},
   Abstract = {A survey paper. However, there are some new results.
             Building on the results in A duality theorm for Willmore
             surfaces, I use the Klein correspondance to determine the
             moduli space of Willmore critical spheres for low critical
             values and also determine the moduli space of Willmore
             minima for the real projective plane in 3-space.},
   Key = {fds318277}
}

@article{fds318278,
   Author = {Bryant, R},
   Title = {Surfaces of mean curvature one in hyperbolic
             space},
   Volume = {154-155},
   Series = {Astérisque},
   Pages = {321-347},
   Booktitle = {Théorie des variétés minimales et applications
             (Palaiseau, 1983–1984)},
   Publisher = {Société Mathématique de France},
   Year = {1988},
   MRNUMBER = {955072},
   url = {http://www.ams.org/mathscinet-getitem?mr=955072},
   Key = {fds318278}
}

@article{fds243397,
   Author = {Bryant, RL},
   Title = {Metrics with exceptional holonomy},
   Journal = {Ann. of Math. (2)},
   Volume = {126},
   Number = {3},
   Pages = {525-576},
   Year = {1987},
   MRNUMBER = {89b:53084},
   url = {http://www.ams.org/mathscinet-getitem?mr=89b:53084},
   Key = {fds243397}
}

@book{fds318279,
   Author = {R. Bryant and Victor Guillemin and Sigurdur Helgason and R. O. Wells, Jr.},
   Title = {Integral Geometry},
   Volume = {63},
   Pages = {350 pages},
   Publisher = {American Mathematical Society},
   Editor = {Bryant, R and Guillemin, V and Helgason, S and Wells,
             RO},
   Year = {1987},
   ISBN = {0-8218-5071-7},
   MRNUMBER = {87j:53003},
   url = {http://www.ams.org/mathscinet-getitem?mr=87j:53003},
   Abstract = {Proceedings of the AMS-IMS-SIAM joint summer research
             conference held in Brunswick, Maine, August 12–18,
             1984},
   Key = {fds318279}
}

@article{fds318280,
   Author = {Bryant, R},
   Title = {On notions of equivalence of variational problems with one
             independent variable},
   Volume = {68},
   Series = {Contemporary Mathematics},
   Pages = {65-76},
   Booktitle = {Differential geometry: the interface between pure and
             applied mathematics (San Antonio, Tex., 1986)},
   Publisher = {American Mathematical Society},
   Editor = {Luksic, M and Martin, C and Shadwick, W},
   Year = {1987},
   ISBN = {0-8218-5075-X},
   MRNUMBER = {89f:58037},
   url = {http://www.ams.org/mathscinet-getitem?mr=89f:58037},
   Key = {fds318280}
}

@article{fds318281,
   Author = {Bryant, R},
   Title = {A survey of Riemannian metrics with special holonomy
             groups},
   Pages = {505-514},
   Booktitle = {Proceedings of the International Congress of Mathematicians.
             Vol. 1, 2. (Berkeley, Calif., 1986)},
   Publisher = {American Mathematical Society},
   Editor = {Gleason, A},
   Year = {1987},
   ISBN = {0-8218-0110-4},
   MRNUMBER = {89f:53068},
   url = {http://www.ams.org/mathscinet-getitem?mr=89f:53068},
   Key = {fds318281}
}

@article{fds318282,
   Author = {Bryant, R},
   Title = {Minimal Lagrangian submanifolds of Kähler-Einstein
             manifolds},
   Volume = {1255},
   Series = {Lecture Notes in Math.},
   Pages = {1-12},
   Booktitle = {Differential geometry and differential equations (Shanghai,
             1985)},
   Publisher = {Springer Verlag},
   Editor = {Gu, C and Berger, M and Bryant, RL},
   Year = {1987},
   ISBN = {3-540-17849-X},
   MRNUMBER = {88j:53061},
   url = {http://www.ams.org/mathscinet-getitem?mr=88j:53061},
   Key = {fds318282}
}

@article{fds243396,
   Author = {R. Bryant and Griffiths, PA and Bryant, RL},
   Title = {Reduction for constrained variational problems and
             $\int{1\over 2}k\sp 2\,ds$},
   Journal = {Amer. J. Math.},
   Volume = {108},
   Number = {3},
   Pages = {525-570},
   Year = {1986},
   MRNUMBER = {88a:58044},
   url = {http://www.ams.org/mathscinet-getitem?mr=88a:58044},
   Key = {fds243396}
}

@article{fds243394,
   Author = {Bryant, RL},
   Title = {Minimal surfaces of constant curvature in
             S^n},
   Journal = {Trans. Amer. Math. Soc.},
   Volume = {290},
   Number = {1},
   Pages = {259-271},
   Year = {1985},
   MRNUMBER = {87c:53110},
   url = {http://www.ams.org/mathscinet-getitem?mr=87c:53110},
   Key = {fds243394}
}

@article{fds243395,
   Author = {Bryant, RL},
   Title = {Lie groups and twistor spaces},
   Journal = {Duke Math. J.},
   Volume = {52},
   Number = {1},
   Pages = {223-261},
   Year = {1985},
   MRNUMBER = {87d:58047},
   url = {http://www.ams.org/mathscinet-getitem?mr=87d:58047},
   Key = {fds243395}
}

@article{fds318283,
   Author = {Bryant, R},
   Title = {Metrics with holonomy G2 or Spin(7)},
   Volume = {1111},
   Series = {Lecture Notes in Math.},
   Pages = {269-277},
   Booktitle = {Workshop Bonn 1984 (Bonn, 1984)},
   Publisher = {Springer},
   Editor = {Hirzebruch, F and Schwermer, J and Suter, S},
   Year = {1985},
   MRNUMBER = {87a:53082},
   url = {http://www.ams.org/mathscinet-getitem?mr=87a:53082},
   Key = {fds318283}
}

@article{fds243393,
   Author = {Bryant, RL},
   Title = {A duality theorem for Willmore surfaces},
   Journal = {J. Differential Geom.},
   Volume = {20},
   Number = {1},
   Pages = {23-53},
   Year = {1984},
   MRNUMBER = {86j:58029},
   url = {http://www.ams.org/mathscinet-getitem?mr=86j:58029},
   Key = {fds243393}
}

@article{fds243391,
   Author = {R. Bryant and Griffiths, P and Yang, D},
   Title = {Characteristics and existence of isometric
             embeddings},
   Journal = {Duke Math. J.},
   Volume = {50},
   Number = {4},
   Pages = {893-994},
   Year = {1983},
   MRNUMBER = {85d:53027},
   url = {http://www.ams.org/mathscinet-getitem?mr=85d:53027},
   Key = {fds243391}
}

@article{fds243392,
   Author = {R. Bryant and Berger, E and Griffiths, P},
   Title = {The Gauss equations and rigidity of isometric
             embeddings},
   Journal = {Duke Math. J.},
   Volume = {50},
   Number = {3},
   Pages = {803-892},
   Year = {1983},
   MRNUMBER = {85k:53056},
   url = {http://www.ams.org/mathscinet-getitem?mr=85k:53056},
   Key = {fds243392}
}

@article{fds318284,
   Author = {R. Bryant and Bryant, R and Griffiths, PA},
   Title = {Some observations on the infinitesimal period relations for
             regular threefolds with trivial canonical
             bundle},
   Volume = {36},
   Series = {Progress in Mathematics},
   Pages = {77-102},
   Booktitle = {Arithmetic and geometry, Vol. II},
   Publisher = {Birkhäuser Boston},
   Editor = {Artin, M and Tate, J},
   Year = {1983},
   ISBN = {3-7643-3133-X},
   MRNUMBER = {86a:32044},
   url = {http://www.ams.org/mathscinet-getitem?mr=86a:32044},
   Key = {fds318284}
}

@article{fds243389,
   Author = {Bryant, RL},
   Title = {Holomorphic curves in Lorentzian CR-manifolds},
   Journal = {Trans. Amer. Math. Soc.},
   Volume = {272},
   Number = {1},
   Pages = {203-221},
   Year = {1982},
   MRNUMBER = {83i:32029},
   url = {http://www.ams.org/mathscinet-getitem?mr=83i:32029},
   Abstract = {When can a real hypersurface in complex n-space contain any
             complex curves? Since the tangent spaces to such a curve
             would have to be null vectors for the Levi form, a necessary
             condition is that the Levi form have zeros. The simplest way
             this can happen in the non-degenerate case is for the Levi
             form to have the Lorentzian signature. In this paper, I show
             that a Lorentzian CR-manifold M has at most a finite
             parameter family of holomorphic curves, in fact, at most an
             n2 parameter family if the dimension of M is 2n+1. This
             maximum is attained, as I show by example. When n=2, the
             only way it can be reached is for M to be CR-flat. In higher
             dimensions, where the CR-flat model does not achieve the
             maximum, it is still unknown whether or not there is more
             than one local model with the maximal dimension family of
             holomorphic curves. The technique used is exterior
             differential systems together with the Chern-Moser theory in
             the n=2 case. Reprints are available, but can also be
             downloaded from the AMS or from JSTOR},
   Key = {fds243389}
}

@article{fds243390,
   Author = {Bryant, RL},
   Title = {Submanifolds and special structures on the
             octonians},
   Journal = {J. Differential Geom.},
   Volume = {17},
   Number = {2},
   Pages = {185-232},
   Year = {1982},
   MRNUMBER = {84h:53091},
   url = {http://www.ams.org/mathscinet-getitem?mr=84h:53091},
   Abstract = {A study of the geometry of submanifolds of real 8-space
             under the group of motions generated by translations and
             rotations in the subgroup Spin(7) instead of the full SO(8).
             I call real 8-space endowed with this group O or octonian
             space. The fact that the stabilizer of an oriented 2-plane
             in Spin(7) is U(3) implies that any oriented 6-manifold in O
             inherits a U(3)-structure. The first part of the paper
             studies the generality of the 6-manifolds whose inherited
             U(3)-structure is symplectic, complex, or Kähler, etc.
             by applying the theory of exterior differential systems. I
             then turn to the study of the standard 6-sphere in O as an
             almost complex manifold and study the space of what are now
             called pseudo-holomorphic curves in the 6-sphere. I prove
             that every compact Riemann surface occurs as a (possibly
             ramified) pseudo-holomorphic curve in the 6-sphere. I also
             show that all of the genus zero pseudo-holomorphic curves in
             the 6-sphere are algebraic as surfaces. Reprints are
             available.},
   Key = {fds243390}
}

@article{fds243410,
   Author = {Bryant, RL},
   Title = {Conformal and minimal immersions of compact surfaces into
             the 4-sphere},
   Journal = {J. Differential Geom.},
   Volume = {17},
   Number = {3},
   Pages = {455-473},
   Year = {1982},
   MRNUMBER = {84a:53062},
   url = {http://www.ams.org/mathscinet-getitem?mr=84a:53062},
   Key = {fds243410}
}

@article{fds318285,
   Author = {R. Bryant and Bryant, R and Chern, SS and Griffiths, PA},
   Title = {Exterior Differential Systems},
   Volume = {1},
   Pages = {219-338},
   Booktitle = {Proceedings of the 1980 Beijing Symposium on Differential
             Geometry and Differential Equations (Beijing,
             1980)},
   Publisher = {Science Press; Gordon & Breach Science Publishers},
   Editor = {Chern, SS and Wu, WT},
   Year = {1982},
   ISBN = {0-677-16420-3},
   MRNUMBER = {85k:58005},
   url = {http://www.ams.org/mathscinet-getitem?mr=85k:58005},
   Key = {fds318285}
}

@article{fds243388,
   Author = {R. Bryant and Berger, E and Griffiths, P},
   Title = {Some isometric embedding and rigidity results for Riemannian
             manifolds},
   Journal = {Proc. Nat. Acad. Sci. U.S.A.},
   Volume = {78},
   Number = {8},
   Pages = {4657-4660},
   Year = {1981},
   MRNUMBER = {82h:53074},
   url = {http://www.ams.org/mathscinet-getitem?mr=82h:53074},
   Key = {fds243388}
}

@book{fds10113,
   Author = {R. Bryant and Marcel Berger and Chao Hao Gu},
   Title = {Differential Geometry and Differential Equations},
   Journal = {Proceedings of the sixth symposium held at Fudan University,
             Shanghai, June 21--July 6, 1985, pp. xii+243, 1987,
             Springer-Verlag, Berlin},
   MRNUMBER = {88b:53002},
   url = {http://www.ams.org/mathscinet-getitem?mr=88b:53002},
   Key = {fds10113}
}

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320