%% Books
@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/mathscinetgetitem?mr=92h:58007},
Abstract = {This book gives a treatment of exterior differential
systems.},
Key = {fds318258}
}
@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}
}
@book{fds318267,
Author = {R. Bryant and David Bao and S.S. Chern and Zhongmin Shen},
Title = {A Sampler of RiemannFinsler Geometry},
Volume = {50},
Series = {Mathematical Sciences Research Institute
Publications},
Pages = {363 pages},
Publisher = {Cambridge University Press},
Editor = {Bao, D and Bryant, RL and Chern, SS and Shen, Z},
Year = {2004},
Month = {November},
ISBN = {0521831814},
MRNUMBER = {MR2132655(2005j:53003)},
url = {http://www.ams.org/mathscinetgetitem?mr=2132655},
Abstract = {These expository accounts treat issues in Finsler geometry
related to volume, geodesics, curvature and mathematical
biology, with instructive examples.},
Key = {fds318267}
}
@book{fds318268,
Author = {R. Bryant and Bryant, R and Griffiths, P and Grossman, D},
Title = {Exterior Differential Systems and EulerLagrange 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 = {The book also covers the Second Variation, EulerLagrange
PDE systems, and higherorder conservation
laws.},
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/mathscinetgetitem?mr=2005e:01025d},
Key = {fds43013}
}
@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 = {0821850717},
MRNUMBER = {87j:53003},
url = {http://www.ams.org/mathscinetgetitem?mr=87j:53003},
Abstract = {Proceedings of the AMSIMSSIAM joint summer research
conference held in Brunswick, Maine, August 12–18,
1984},
Key = {fds318279}
}
@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 21July 6, 1985, pp. xii+243, 1987,
SpringerVerlag, Berlin},
MRNUMBER = {88b:53002},
url = {http://www.ams.org/mathscinetgetitem?mr=88b:53002},
Key = {fds10113}
}
%% Papers Published
@article{fds345423,
Author = {Bryant, R and Buckmire, R and Khadjavi, L and Lind,
D},
Title = {The origins of spectra, an organization for LGBT
mathematicians},
Journal = {Notices of the American Mathematical Society},
Volume = {66},
Number = {6},
Pages = {875882},
Year = {2019},
Month = {June},
url = {http://dx.doi.org/10.1090/noti1890},
Doi = {10.1090/noti1890},
Key = {fds345423}
}
@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 = {345357},
Publisher = {Elsevier BV},
Year = {2017},
Month = {June},
url = {http://dx.doi.org/10.1016/j.geomphys.2017.02.012},
Abstract = {© 2017 Elsevier B.V. We study twodimensional Finsler
metrics of constant flag curvature and show that such
Finsler metrics that admit a Killing field can be written in
a normal form that depends on two arbitrary functions of one
variable. Furthermore, we find an approach to calculate
these functions for spherically symmetric Finsler surfaces
of constant flag curvature. In particular, we obtain the
normal form of the Funk metric on the unit disk
D2.},
Doi = {10.1016/j.geomphys.2017.02.012},
Key = {fds325462}
}
@article{fds320294,
Author = {Bryant, RL},
Title = {On the convex PfaffDarboux Theorem of Ekeland and
Nirenberg},
Year = {2015},
Month = {December},
url = {http://arxiv.org/abs/1512.07100},
Abstract = {The classical PfaffDarboux Theorem, which provides local
`normal forms' for 1forms 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 PfaffDarboux 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 nspace, convexity has
its usual meaning. In 2002, Ekeland and Nirenberg were able
to characterize necessary and sufficient conditions for a
given 1form 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 PfaffDarboux Theorem, one that covers the case of a
Legendrian foliation in which the notion of convexity is
defined in terms of a torsionfree 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 2tori},
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 almostcomplex structures on the
sixsphere},
Year = {2014},
Month = {May},
url = {http://arxiv.org/abs/1405.3405},
Keywords = {6sphere • complex structure • exceptional
geometry},
Abstract = {In 2003, S.s. Chern began a study of almostcomplex
structures on the 6sphere, with the idea of exploiting the
special properties of its wellknown almostcomplex
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
almostcomplex structure on the 6sphere, he did prove a
significant identity that resolves the question for an
interesting class of almostcomplex structures on the
6sphere.},
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 notsotypical 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 BernsteinGelfandGelfand
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}
}
@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{fds243372,
Author = {Bryant, RL},
Title = {Nonembedding and nonextension results in special
holonomy},
Pages = {346367},
Booktitle = {The Many Facets of Geometry},
Publisher = {Oxford University Press},
Address = {Oxford},
Editor = {GarciaPrada, O and Bourguignon, JP and Salamon,
S},
Year = {2010},
Month = {Fall},
ISBN = {9780199534920},
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 wellposed for
smooth initial data and counterexamples to existence are
constructed.},
Doi = {10.1093/acprof:oso/9780199534920.003.0017},
Key = {fds243372}
}
@article{fds243378,
Author = {R. Bryant and Bryant, RL and Dunajski, M and Eastwood, M},
Title = {Metrisability of twodimensional projective
structures},
Volume = {83},
Number = {3},
Pages = {465500},
Publisher = {International Press of Boston},
Year = {2009},
Month = {November},
ISSN = {0022040X},
MRCLASS = {53},
MRNUMBER = {MR2581355},
url = {http://dx.doi.org/10.4310/jdg/1264601033},
Abstract = {We carry out the programme of R. Liouville \cite{Liouville}
to construct an explicit local obstruction to the existence
of a LeviCivita 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.},
Doi = {10.4310/jdg/1264601033},
Key = {fds243378}
}
@article{fds243377,
Author = {Bryant, RL},
Title = {Commentary},
Journal = {Bulletin of the American Mathematical Society},
Volume = {46},
Number = {2},
Pages = {177178},
Publisher = {American Mathematical Society (AMS)},
Year = {2009},
Month = {April},
ISSN = {02730979},
url = {http://dx.doi.org/10.1090/S0273097909012488},
Doi = {10.1090/S0273097909012488},
Key = {fds243377}
}
@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
twodimensional metrics admitting two projective vector
fields},
Journal = {Mathematische Annalen},
Volume = {340},
Number = {2},
Pages = {437463},
Publisher = {Springer Nature America, Inc},
Year = {2008},
Month = {Spring},
url = {http://www.arxiv.org/abs/0705.3592},
Abstract = {We give a complete list of normal forms for the
twodimensional metrics that admit a transitive Lie
pseudogroup of geodesicpreserving transformations and we
show that these normal forms are mutually nonisometric.
This solves a problem posed by Sophus Lie. © 2007
SpringerVerlag.},
Doi = {10.1007/s0020800701583},
Key = {fds243385}
}
@article{fds320198,
Author = {Bryant, RL},
Title = {Gradient Kähler Ricci solitons},
Journal = {Astérisque},
Volume = {321},
Series = {Astérisque},
Number = {321},
Pages = {5197},
Booktitle = {Géométrie différentielle, physique mathématique,
mathématiques et société. I.},
Publisher = {Soc. Math. France},
Year = {2008},
Month = {Spring},
ISBN = {9782856292587},
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}
}
@article{fds318260,
Author = {BRYANT, RL},
Title = {Conformal geometry and 3plane fields on
6manifolds},
Journal = {Rims Kokyuroku},
Volume = {1502 (Developments of Cartan Geometry an},
Series = {RIMS Symposium Proceedings},
Pages = {115},
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
3plane fields D on 6manifolds 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 Hbundle over M where
H is the subgroup of SO(4,3) that stabilizes a null 3plane
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{fds243386,
Author = {Bryant, RL},
Title = {On the geometry of almost complex 6manifolds},
Journal = {Asian Journal of Mathematics},
Volume = {10},
Number = {3},
Pages = {561605},
Publisher = {International Press of Boston},
Year = {2006},
Month = {January},
url = {http://dx.doi.org/10.4310/AJM.2006.v10.n3.a4},
Keywords = {almost complex manifolds • quasiintegrable •
Nijenhuis tensor},
Abstract = {This article discusses some basic geometry of almost complex
6manifolds. A 2parameter family of intrinsic firstorder
functionals on almost complex structures on 6manifolds is
introduced and their EulerLagrange equations are computed.
A natural generalization of holomorphic bundles over complex
manifolds to the almost complex case is introduced. The
general almost complex manifold will not admit any
nontrivial bundles of this type, but there is a class of
nonintegrable almost complex manifolds for which there are
such nontrivial bundles. For example, the G2invariant
almost complex structure on the 6sphere admits such
nontrivial bundles. This class of almost complex manifolds
in dimension 6 will be referred to as quasiintegrable and a
corresponding condition for unitary structures is
considered. Some of the properties of quasiintegrable
structures (both almost complex and unitary) are developed
and some examples are given. However, it turns out that
quasiintegrability is not an involutive condition, so the
full generality of these structures in Cartan's sense is not
wellunderstood. The failure of this involutivity is
discussed and some constructions are made to show, at least
partially, how general these structures can be. © 2006
Robert L. Bryant.},
Doi = {10.4310/AJM.2006.v10.n3.a4},
Key = {fds243386}
}
@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 = {95112},
Publisher = {Springer Nature},
Year = {2006},
Month = {January},
MRNUMBER = {MR2209954},
url = {http://dx.doi.org/10.1007/s1140100503685},
Keywords = {calibrations, special Lagrangian submanifolds},
Abstract = {Let SO(n) act in the standard way on ℂn and extend this
action in the usual way to ℂn+1 = ℂ ⊕ ℂ n . It is
shown that a nonsingular special Lagrangian submanifold L
⊂ ℂn+1 that is invariant under this SO(n)action
intersects the fixed ℂ ⊂ ℂ n+1 in a nonsingular
realanalytic arc A (which may be empty). If n > 2, then A
has no compact component. Conversely, an embedded,
noncompact nonsingular realanalytic arc A ⊂ 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 Gérard
and Tahara to prove the existence of the extension. © The
Editorial Office of CAM and SpringerVerlag Berlin
Heidelberg 2006.},
Doi = {10.1007/s1140100503685},
Key = {fds243387}
}
@article{fds318261,
Author = {Bryant, R and Freed, D},
Title = {ShiingShen Chern},
Journal = {Physics Today},
Volume = {59},
Number = {1},
Pages = {7072},
Publisher = {AIP Publishing},
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
3folds},
Journal = {Perspectives in Riemannian Geometry},
Volume = {40},
Series = {CRM Proceedings and Lecture Notes},
Pages = {6398},
Booktitle = {Perspectives in Riemannian Geometry},
Publisher = {AMER MATHEMATICAL SOC},
Editor = {Apostolov, V and Dancer, A and Hitchin, N and Wang,
M},
Year = {2006},
Month = {January},
ISBN = {0821838520},
url = {http://arxiv.org/abs/math/0007128},
Abstract = {A second order family of special Lagrangian submanifolds of
complex mspace 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 3space 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 LawlorHarvey
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 = {Surveys on Discrete and Computational Geometry: Twenty Years
Later},
Volume = {395},
Series = {Contemporary Mathematics},
Pages = {2938},
Booktitle = {150 years of mathematics at Washington University in St.
Louis},
Publisher = {AMER MATHEMATICAL SOC},
Editor = {Jensen, GR and Krantz, SG},
Year = {2006},
Month = {January},
ISBN = {082183603X},
MRNUMBER = {MR2206889},
url = {http://www.ams.org/mathscinetgetitem?mr=2206889},
Keywords = {53C29 (70F25)},
Key = {fds318263}
}
@article{fds318264,
Author = {Bryant, R},
Title = {Geodesically reversible Finsler 2spheres of constant
curvature},
Volume = {11},
Series = {Nankai Tracts in Mathematics},
Pages = {95111},
Booktitle = {Inspired by S. S. ChernA 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 2sphere 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 2sphere 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_2structures},
Pages = {75109},
Booktitle = {Proceedings of Gökova GeometryTopology Conference
2005},
Publisher = {International Press},
Editor = {Akbulut, S and Onder, T and Stern, R},
Year = {2006},
ISBN = {1571461523},
url = {http://arxiv.org/abs/math/0305124},
Abstract = {This article consists of some loosely related remarks about
the geometry of G_2structures on 7manifolds 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_2structure in terms of its torsion. When the fundamental
3form of the G_2structure 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 torsionfree. This version contains some new
results on the pinching of Ricci curvature for metrics
associated to closed G_2structures. 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 longtime 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 = {7190},
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 = {1571461752},
MRNUMBER = {MR2205367},
url = {http://www.ams.org/mathscinetgetitem?mr=2205367},
Key = {fds318266}
}
@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 2manifold X
endowed with a holomorphic volume form. A strictly
pseudoconvex real hypersurface M in X inherits not only a
CRstructure 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 spacefilling diagram},
Journal = {Discrete & Computational Geometry},
Volume = {32},
Number = {3},
Pages = {293308},
Publisher = {Springer Nature},
Year = {2004},
Month = {January},
MRNUMBER = {2005k:92077},
url = {http://dx.doi.org/10.1007/s0045400410991},
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
spacefilling 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
inclusionexclusion formulas for these sizes.},
Doi = {10.1007/s0045400410991},
Key = {fds243379}
}
@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 = {221262},
Publisher = {UNIV HOUSTON},
Year = {2002},
Month = {January},
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 nmanifold
of constant positive flag curvature out of a hypersurface in
suitably general position in complex projective nspace. The
third remark is that there is a description of the Finsler
metrics of constant curvature on the 2sphere in terms of a
Riemannian metric and 1form on the space of its geodesics.
In particular, this allows one to use any (Riemannian) Zoll
metric of positive Gauss curvature on the 2sphere to
construct a global Finsler metric of constant positive
curvature on the 2sphere. 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
2nmanifolds. As a by product, it is found that these
groups do occur as the holonomy of torsionfree affine
connections in dimension 2n, a hitherto unsuspected
phenomenon. },
Key = {fds243380}
}
@article{fds10364,
Title = {Leviflat minimal hypersurfaces in twodimensional complex
space forms},
Volume = {37},
Series = {Adv. Stud. Pure Math.},
Pages = {144},
Booktitle = {Lie groups, geometric structures and differential
equationsone 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 Leviflat and minimal. The main results are as follows:
When the curvature of the complex space form is nonzero,
there is a 1parameter family of such hypersurfaces.
Specifically, for each oneparameter subgroup of the
isometry group of the complex space form, there is an
essentially unique example that is invariant under this
oneparameter subgroup. On the other hand, when the
curvature of the space form is zero, i.e., when the space
form is complex 2space 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{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 = {14},
Pages = {88121},
Publisher = {Springer Nature},
Year = {2001},
Month = {October},
MRNUMBER = {2002i:53010},
url = {http://dx.doi.org/10.1007/BF03322701},
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.},
Doi = {10.1007/BF03322701},
Key = {MR2002i:53010}
}
@article{fds243382,
Author = {Bryant, RL},
Title = {Bochnerkähler metrics},
Journal = {Journal of the American Mathematical Society},
Volume = {14},
Number = {3},
Pages = {623715},
Year = {2001},
Month = {July},
MRNUMBER = {2002i:53096},
url = {http://dx.doi.org/10.1090/S0894034701003666},
Abstract = {A Kahler metric is said to be BochnerKahler 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 BochnerKahler metrics in
complex dimension n has real dimension n+1 and a recipe for
an explicit formula for any BochnerKahler metric is given.
It is shown that any BochnerKahler metric in complex
dimension n has local (real) cohomogeneity at most~n. The
BochnerKahler 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 BochnerKahler
metric. The fundamental technique is to construct a
canonical infinitesimal torus action on a BochnerKahler
metric whose associated momentum mapping has the orbits of
its symmetry pseudogroupoid as fibers.},
Doi = {10.1090/S0894034701003666},
Key = {fds243382}
}
@article{fds320301,
Author = {Bryant, RL},
Title = {Rigidity and quasirigidity 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 quasirigid (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{fds243383,
Author = {Bryant, R},
Title = {Recent advances in the theory of holonomy},
Journal = {Astérisque},
Volume = {266},
Number = {5},
Pages = {351374},
Publisher = {Centre National de la Recherche Scientifique},
Year = {2000},
Month = {December},
MRNUMBER = {2001h:53067},
url = {http://www.dmi.ens.fr/bourbaki/Prog_juin99.html},
Abstract = {After its introduction by Élie Cartan, the notion of
holonomy has become increasingly important in Riemannian and
affine geometry. Beginning with the fundamental work of
Marcel Berger, the classification of possible holonomy
groups of torsion free connections, either Riemannian or
affine, has continued to be developed, with major
breakthroughs in the last ten years. I will report on the
local classification in the affine case, Joyce's fundamental
work on compact manifolds with exceptional holonomies and
their associated geometries, and some new work on the
classification of holonomies of connections with restricted
torsion, which has recently become of interest in string
theory.},
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 = {219265},
Publisher = {International Press of Boston},
Year = {2000},
Month = {January},
MRNUMBER = {2001i:53101},
url = {http://dx.doi.org/10.4310/CAG.2000.v8.n2.a1},
Abstract = {The harmonic morphisms φ : Mn+1 → Nn are studied using
the methods of the moving frame and exterior differential
systems and three main results are achieved. The first
result is a local structure theorem for such maps in the
case that φ is a submersion, in particular, a normal form
is found for all such φ once the metric on the target
manifold N is specified. The second result is a finiteness
theorem, which says, in a certain sense, that, when n ≥ 3,
the set of harmonic morphisms with a given Riemannian domain
(Mn+1,g) is a finite dimensional space. The third result is
the explicit classification when n ≥ 3 of all local and
global harmonic morphisms with domain (Mn+1,g), a space of
constant curvature.},
Doi = {10.4310/CAG.2000.v8.n2.a1},
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 = {34},
Pages = {405435},
Year = {2000},
MRNUMBER = {2002j:53063},
url = {http://arxiv.org/abs/math/9912246},
Abstract = {Every closed, oriented, real analytic Riemannian 3manifold
can be isometrically embedded as a special Lagrangian
submanifold of a CalabiYau 3fold, even as the real locus
of an antiholomorphic, isometric involution. Every closed,
oriented, real analytic Riemannian 4manifold whose bundle
of selfdual 2forms is trivial can be isometrically
embedded as a coassociative submanifold in a G_2manifold,
even as the fixed locus of an antiG_2 involution. These
results, when coupled with McLean's analysis of the moduli
spaces of such calibrated submanifolds, 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 = {520},
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, R},
Title = {PseudoReimannian metrics with parallel spinor fields and
vanishing Ricci tensor},
Volume = {4},
Series = {Séminaires & Congrès},
Pages = {5394},
Booktitle = {Global analysis and harmonic analysis (MarseilleLuminy,
1999)},
Publisher = {Société Mathématique de France},
Editor = {Bourguinon, JP and Branson, T and Hijazi, O},
Year = {2000},
ISBN = {2856290949},
MRNUMBER = {2002h:53082},
url = {http://arxiv.org/abs/math/0004073},
Abstract = {I discuss geometry and normal forms for pseudoRiemannian
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 pseudoRiemannian
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 = {Advances in Theoretical and Mathematical
Physics},
Volume = {3},
Number = {1},
Pages = {8390},
Publisher = {International Press of Boston},
Year = {1999},
Month = {January},
MRNUMBER = {2000f:32033},
url = {http://dx.doi.org/10.4310/ATMP.1999.v3.n1.a2},
Abstract = {A short paper giving some examples of smooth hypersurfaces M
of degree n+1 in complex projective nspace that are defined
by real polynomial equations and whose real slice contains a
component diffeomorphic to an n1 torus, which is then
special Lagrangian with respect to the CalabiYau metric on
M.},
Doi = {10.4310/ATMP.1999.v3.n1.a2},
Key = {fds243402}
}
@article{fds243408,
Author = {R. Bryant and Bryant, RL and Sharpe, E},
Title = {Dbranes and Spin^{c} structures},
Journal = {Physics Letters B},
Volume = {450},
Number = {4},
Pages = {353357},
Publisher = {Elsevier BV},
Year = {1999},
Month = {January},
MRNUMBER = {2000c:53054},
url = {http://dx.doi.org/10.1016/S03702693(99)001616},
Abstract = {It was recently pointed out by E. Witten that for a Dbrane
to consistently wrap a submanifold of some manifold, the
normal bundle must admit a Spinc 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 supersymmetric cycle is
automatically Spinc. © 1999 Published by Elsevier Science
B.V. All rights reserved.},
Doi = {10.1016/S03702693(99)001616},
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/mathscinetgetitem?mr=99f:90029},
Key = {fds10011}
}
@article{fds243403,
Author = {Bryant, RL},
Title = {Projectively flat finsler 2spheres of constant
curvature},
Journal = {Selecta Mathematica},
Volume = {3},
Number = {2},
Pages = {161203},
Publisher = {Springer Nature},
Year = {1997},
Month = {January},
MRNUMBER = {98i:53101},
url = {http://dx.doi.org/10.1007/s000290050009},
Abstract = {After recalling the structure equations of Finsler
structures on surfaces, I define a notion of "generalized
Finsler structure" as a way of microlocalizing the problem
of describing Finsler structures subject to curvature
conditions. I then recall the basic notions of path geometry
on a surface and define a notion of "generalized path
geometry" analogous to that of "generalized Finsler
structure." I use these ideas to study the geometry of
Finsler structures on the 2sphere that have constant
FinslerGauss curvature K and whose geodesic path geometry
is projectively flat, i.e., locally equivalent to that of
straight lines in the plane. I show that, modulo
diffeomorphism, there is a 2parameter family of
projectively flat Finsler structures on the sphere whose
FinslerGauss curvature K is identically 1. © Birkhäuser
Verlag, 1997.},
Doi = {10.1007/s000290050009},
Key = {fds243403}
}
@article{fds8915,
Title = {Finsler structures on the 2sphere 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 Shiingshen Chern and Zhongmin
Shen},
Year = {1996},
MRNUMBER = {97e:53128},
url = {http://www.math.duke.edu/preprints/9511.dvi},
Key = {fds8915}
}
@article{fds318271,
Author = {Bryant, R},
Title = {On extremals with prescribed Lagrangian densities},
Volume = {36},
Series = {Symposia Mathematica},
Pages = {86111},
Booktitle = {Manifolds and geometry (Pisa, 1993)},
Publisher = {Cambridge University Press},
Editor = {Bartolomeis, P and Tricerri, F and Vesentini, E},
Year = {1996},
ISBN = {0521562163},
MRNUMBER = {99a:58043},
url = {http://arxiv.org/abs/dgga/9406001},
Abstract = {This article studies some examples of the family of problems
where a Lagrangian is given for maps from one manifold to
another and one is interested in the extremal mappings for
which the Lagrangian density takes a prescribed form. The
first problem is the study of when two minimal graphs can
induce the same area function on the domain without
differing by trivial symmetries. The second problem is
similar but concerns a different `area Lagrangian' first
investigated by Calabi. The third problem classified the
harmonic maps between spheres (more generally, manifolds of
constant sectional curvature) for which the energy density
is a constant multiple of the volume form. In the first and
third cases, the complete solution is described. In the
second case, some information about the solutions is
derived, but the problem is not completely
solved.},
Key = {fds318271}
}
@article{fds318272,
Author = {Bryant, R},
Title = {Classical, exceptional, and exotic holonomies: a status
report},
Volume = {1},
Series = {Sémin. Congr.},
Pages = {93165},
Booktitle = {Actes de la Table Ronde de Géométrie Différentielle},
Publisher = {Société Mathématique de France},
Editor = {Besse, A},
Year = {1996},
ISBN = {2856290477},
MRNUMBER = {98c:53037},
url = {http://www.math.duke.edu/preprints/9510.dvi},
Abstract = {A survey paper on the status of the holonomy problem as of
1995.},
Key = {fds318272}
}
@article{fds243404,
Author = {R. Bryant and Bryant, R and Griffiths, P and Hsu, L},
Title = {Hyperbolic exterior differential systems and their
conservation laws, part II},
Journal = {Selecta Mathematica},
Volume = {1},
Number = {2},
Pages = {265323},
Publisher = {Springer Nature},
Year = {1995},
Month = {September},
MRNUMBER = {97d:580009},
url = {http://www.math.duke.edu/preprints/9413.dvi},
Doi = {10.1007/BF01671567},
Key = {fds243404}
}
@article{fds243407,
Author = {R. Bryant and Bryant, RL and Griffiths, PA},
Title = {Characteristic cohomology of differential systems. I.
General theory},
Journal = {Journal of the American Mathematical Society},
Volume = {8},
Number = {3},
Pages = {507507},
Publisher = {American Mathematical Society (AMS)},
Year = {1995},
Month = {September},
MRNUMBER = {96c:58183},
url = {http://www.math.duke.edu/preprints/9301.dvi},
Doi = {10.1090/s0894034719951311820x},
Key = {fds243407}
}
@article{fds243405,
Author = {R. Bryant and Bryant, R and Griffiths, P and Hsu, L},
Title = {Hyperbolic exterior differential systems and their
conservation laws, part I},
Journal = {Selecta Mathematica},
Volume = {1},
Number = {1},
Pages = {21112},
Publisher = {Springer Nature},
Year = {1995},
Month = {March},
MRNUMBER = {97d:580008},
url = {http://www.math.duke.edu/preprints/9413.dvi},
Doi = {10.1007/BF01614073},
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 Mathematical Journal},
Volume = {78},
Number = {3},
Pages = {531676},
Publisher = {Duke University Press},
Year = {1995},
Month = {January},
MRNUMBER = {96d:58158},
url = {http://www.math.duke.edu/preprints/9302.dvi},
Doi = {10.1215/S0012709495078247},
Key = {fds243406}
}
@article{fds318273,
Author = {R. Bryant and BRYANT, R and GRIFFITHS, P and HSU, L},
Title = {TOWARD A GEOMETRY OF DIFFERENTIALEQUATIONS},
Journal = {Geometry, Topology & Physics},
Volume = {4},
Series = {Conf. Proc. Lecture Notes Geom. Topology},
Pages = {176},
Booktitle = {Geometry, Topology, & Physics},
Publisher = {INTERNATIONAL PRESS INC BOSTON},
Editor = {Yau, ST},
Year = {1995},
Month = {January},
ISBN = {1571460241},
MRNUMBER = {97b:58005},
url = {http://www.math.duke.edu/preprints/9412.dvi},
Key = {fds318273}
}
@article{fds318274,
Author = {R. Bryant and Bryant, R and Gardner, RB},
Title = {Control Structures},
Volume = {12},
Series = {Banach Center Publications},
Pages = {111121},
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/9411.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 = {5181},
Booktitle = {Geometry and quantum field theory (Park City, UT,
1991)},
Publisher = {American Mathematical Society},
Editor = {Freed, D and Uhlenbeck, K},
Year = {1995},
ISBN = {0821804006},
MRNUMBER = {96i:58002},
url = {http://www.ams.org/mathscinetgetitem?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 = {435461},
Publisher = {Springer Nature},
Year = {1993},
Month = {December},
ISSN = {00209910},
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 = {Boletim Da Sociedade Brasileira De Matem�Tica},
Volume = {21},
Number = {2},
Pages = {133157},
Publisher = {Springer Nature},
Year = {1991},
Month = {September},
MRNUMBER = {92k:53112},
url = {http://www.math.duke.edu/preprints/9003.dvi},
Abstract = {We prove several structure theorems about the special class
of minimal submanifolds which Harvey and Lawson have called
"austere" and which arose in connection with their
foundational work on calibrations. The condition of
austerity is a pontwise condition on the second fundamental
form and essentially requires that the nonzero eigenvalues
of the second fundamental form in any normal direction at
any point occur in oppositely signed pairs. We solve the
pointwise problem of describing the set of austere second
fundamental forms in dimension at most four and the local
problem of describing the austere threefolds in Euclidean
space in all dimensions. © 1991 Sociedade Brasileira de
Matemática.},
Doi = {10.1007/BF01237361},
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 = {3388},
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 = {0821814923},
MRNUMBER = {93e:53030},
url = {http://www.math.duke.edu/~bryant/ExoticHol.dvi},
Key = {fds318276}
}
@article{fds243398,
Author = {R. Bryant and Bryant, R and Harvey, R},
Title = {Submanifolds in hyperKähler geometry},
Journal = {Journal of the American Mathematical Society},
Volume = {2},
Number = {1},
Pages = {131},
Publisher = {American Mathematical Society (AMS)},
Year = {1989},
Month = {January},
MRNUMBER = {89m:53090},
url = {http://dx.doi.org/10.1090/S08940347198909531698},
Doi = {10.1090/S08940347198909531698},
Key = {fds243398}
}
@article{fds243399,
Author = {R. Bryant and Bryant, RL and Salamon, SM},
Title = {On the construction of some complete metrics with
exceptional holonomy},
Journal = {Duke Mathematical Journal},
Volume = {58},
Number = {3},
Pages = {829850},
Publisher = {Duke University Press},
Year = {1989},
Month = {January},
MRNUMBER = {90i:53055},
url = {http://dx.doi.org/10.1215/S0012709489058390},
Doi = {10.1215/S0012709489058390},
Key = {fds243399}
}
@article{fds318277,
Author = {Bryant, R},
Title = {Surfaces in conformal geometry},
Volume = {48},
Series = {Proc. Sympos. Pure Math.},
Pages = {227240},
Booktitle = {The mathematical heritage of Hermann Weyl (Durham, NC,
1987)},
Publisher = {American Mathematical Society},
Editor = {Wells, RO},
Year = {1988},
ISBN = {0821814826},
MRNUMBER = {89m:53102},
url = {http://www.ams.org/mathscinetgetitem?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 3space.},
Key = {fds318277}
}
@article{fds318278,
Author = {Bryant, R},
Title = {Surfaces of mean curvature one in hyperbolic
space},
Volume = {154155},
Series = {Astérisque},
Pages = {321347},
Booktitle = {Théorie des variétés minimales et applications
(Palaiseau, 1983–1984)},
Publisher = {Société Mathématique de France},
Year = {1988},
MRNUMBER = {955072},
url = {http://www.ams.org/mathscinetgetitem?mr=955072},
Key = {fds318278}
}
@article{fds243397,
Author = {Bryant, RL},
Title = {Metrics with exceptional holonomy},
Journal = {Ann. of Math. (2)},
Volume = {126},
Number = {3},
Pages = {525576},
Year = {1987},
MRNUMBER = {89b:53084},
url = {http://www.ams.org/mathscinetgetitem?mr=89b:53084},
Key = {fds243397}
}
@article{fds318280,
Author = {Bryant, R},
Title = {On notions of equivalence of variational problems with one
independent variable},
Volume = {68},
Series = {Contemporary Mathematics},
Pages = {6576},
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 = {082185075X},
MRNUMBER = {89f:58037},
url = {http://www.ams.org/mathscinetgetitem?mr=89f:58037},
Key = {fds318280}
}
@article{fds318281,
Author = {Bryant, R},
Title = {A survey of Riemannian metrics with special holonomy
groups},
Pages = {505514},
Booktitle = {Proceedings of the International Congress of Mathematicians.
Vol. 1, 2. (Berkeley, Calif., 1986)},
Publisher = {American Mathematical Society},
Editor = {Gleason, A},
Year = {1987},
ISBN = {0821801104},
MRNUMBER = {89f:53068},
url = {http://www.ams.org/mathscinetgetitem?mr=89f:53068},
Key = {fds318281}
}
@article{fds318282,
Author = {Bryant, R},
Title = {Minimal Lagrangian submanifolds of KählerEinstein
manifolds},
Volume = {1255},
Series = {Lecture Notes in Math.},
Pages = {112},
Booktitle = {Differential geometry and differential equations (Shanghai,
1985)},
Publisher = {SpringerVerlag},
Editor = {Gu, C and Berger, M and Bryant, RL},
Year = {1987},
ISBN = {354017849X},
MRNUMBER = {88j:53061},
url = {http://www.ams.org/mathscinetgetitem?mr=88j:53061},
Key = {fds318282}
}
@article{fds243396,
Author = {R. Bryant and Bryant, R and Griffiths, P},
Title = {Reduction for Constrained Variational Problems and � κ 2
2 ds},
Journal = {American Journal of Mathematics},
Volume = {108},
Number = {3},
Pages = {525525},
Publisher = {JSTOR},
Year = {1986},
Month = {June},
MRNUMBER = {88a:58044},
url = {http://dx.doi.org/10.2307/2374654},
Doi = {10.2307/2374654},
Key = {fds243396}
}
@article{fds243394,
Author = {Bryant, RL},
Title = {Minimal surfaces of constant curvature in
s^{n}},
Journal = {Transactions of the American Mathematical
Society},
Volume = {290},
Number = {1},
Pages = {259271},
Publisher = {American Mathematical Society (AMS)},
Year = {1985},
Month = {January},
MRNUMBER = {87c:53110},
url = {http://dx.doi.org/10.1090/S00029947198507879648},
Abstract = {In this note, we study an overdetermined system of partial
differential equations whose solutions determine the minimal
surfaces in Sn of constant Gaussian curvature. If the
Gaussian curvature is positive, the solution to the global
problem was found by [Calabi], while the solution to the
local problem was found by [Wallach]. The case of
nonpositive Gaussian curvature is more subtle and has
remained open. We prove that there are no minimal surfaces
in Sn of constant negative Gaussian curvature (even
locally). We also find all of the flat minimal surfaces in
Sn and give necessary and sufficient conditions that a given
twotorus may be immersed minimally, conformally, and flatly
into Sn. © 1985 American Mathematical Society.},
Doi = {10.1090/S00029947198507879648},
Key = {fds243394}
}
@article{fds243395,
Author = {Bryant, RL},
Title = {Lie groups and twlstor spaces},
Journal = {Duke Mathematical Journal},
Volume = {52},
Number = {1},
Pages = {223261},
Publisher = {Duke University Press},
Year = {1985},
Month = {January},
MRNUMBER = {87d:58047},
url = {http://dx.doi.org/10.1215/S0012709485052135},
Doi = {10.1215/S0012709485052135},
Key = {fds243395}
}
@article{fds318283,
Author = {Bryant, R},
Title = {Metrics with holonomy G2 or Spin(7)},
Volume = {1111},
Series = {Lecture Notes in Math.},
Pages = {269277},
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/mathscinetgetitem?mr=87a:53082},
Key = {fds318283}
}
@article{fds243393,
Author = {Bryant, RL},
Title = {A duality theorem for willmore surfaces},
Journal = {Journal of Differential Geometry},
Volume = {20},
Number = {1},
Pages = {2353},
Publisher = {International Press of Boston},
Year = {1984},
Month = {January},
MRNUMBER = {86j:58029},
url = {http://dx.doi.org/10.4310/jdg/1214438991},
Doi = {10.4310/jdg/1214438991},
Key = {fds243393}
}
@article{fds243391,
Author = {R. Bryant and Bryant, RL and Griffiths, PA and Yang, D},
Title = {Characteristics and existence of isometric
embeddings},
Journal = {Duke Mathematical Journal},
Volume = {50},
Number = {4},
Pages = {893994},
Publisher = {Duke University Press},
Year = {1983},
Month = {January},
MRNUMBER = {85d:53027},
url = {http://dx.doi.org/10.1215/S0012709483050408},
Doi = {10.1215/S0012709483050408},
Key = {fds243391}
}
@article{fds243392,
Author = {R. Bryant and Berger, E and Bryant, R and Griffiths, P},
Title = {The Gauss equations and rigidity of isometric
embeddings},
Journal = {Duke Mathematical Journal},
Volume = {50},
Number = {3},
Pages = {803892},
Publisher = {Duke University Press},
Year = {1983},
Month = {January},
MRNUMBER = {85k:53056},
url = {http://dx.doi.org/10.1215/S0012709483050391},
Doi = {10.1215/S0012709483050391},
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 = {77102},
Booktitle = {Arithmetic and geometry, Vol. II},
Publisher = {Birkhäuser Boston},
Editor = {Artin, M and Tate, J},
Year = {1983},
ISBN = {376433133X},
MRNUMBER = {86a:32044},
url = {http://www.ams.org/mathscinetgetitem?mr=86a:32044},
Key = {fds318284}
}
@article{fds243389,
Author = {Bryant, RL},
Title = {Holomorphic curves in lorentzian crmanifolds},
Journal = {Transactions of the American Mathematical
Society},
Volume = {272},
Number = {1},
Pages = {203221},
Publisher = {American Mathematical Society (AMS)},
Year = {1982},
Month = {January},
MRNUMBER = {83i:32029},
url = {http://dx.doi.org/10.1090/S00029947198206564864},
Abstract = {A CRmanifold is said to be Lorentzian if its Levi form has
one negative eigenvalue and the rest positive. In this case,
it is possible that the CRmanifold contains holomorphic
curves. In this paper, necessary and sufficient conditions
are derived (in terms of the “derivatives” of the
CRstructure) in order that holomorphic curves exist. A
“flatness” theorem is proven characterizing the real
Lorentzian hyperquadric Qs C CP3and examples are given
showing that nonflat Lorentzian hyperquadrics can have a
richer family of holomorphic curves than the flat ones. ©
1982 American Mathematical Society.},
Doi = {10.1090/S00029947198206564864},
Key = {fds243389}
}
@article{fds243390,
Author = {Bryant, RL},
Title = {Submanifolds and special structures on the
octonians},
Journal = {Journal of Differential Geometry},
Volume = {17},
Number = {2},
Pages = {185232},
Publisher = {International Press of Boston},
Year = {1982},
Month = {January},
MRNUMBER = {84h:53091},
url = {http://dx.doi.org/10.4310/jdg/1214436919},
Abstract = {A study of the geometry of submanifolds of real 8space
under the group of motions generated by translations and
rotations in the subgroup Spin(7) instead of the full SO(8).
I call real 8space endowed with this group O or octonian
space. The fact that the stabilizer of an oriented 2plane
in Spin(7) is U(3) implies that any oriented 6manifold in O
inherits a U(3)structure. The first part of the paper
studies the generality of the 6manifolds 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 6sphere in O as an
almost complex manifold and study the space of what are now
called pseudoholomorphic curves in the 6sphere. I prove
that every compact Riemann surface occurs as a (possibly
ramified) pseudoholomorphic curve in the 6sphere. I also
show that all of the genus zero pseudoholomorphic curves in
the 6sphere are algebraic as surfaces. Reprints are
available.},
Doi = {10.4310/jdg/1214436919},
Key = {fds243390}
}
@article{fds243410,
Author = {Bryant, RL},
Title = {Conformal and minimal immersions of compact surfaces into
the 4sphere},
Journal = {Journal of Differential Geometry},
Volume = {17},
Number = {3},
Pages = {455473},
Publisher = {International Press of Boston},
Year = {1982},
Month = {January},
MRNUMBER = {84a:53062},
url = {http://dx.doi.org/10.4310/jdg/1214437137},
Doi = {10.4310/jdg/1214437137},
Key = {fds243410}
}
@article{fds318285,
Author = {R. Bryant and Bryant, R and Chern, SS and Griffiths, PA},
Title = {Exterior Differential Systems},
Volume = {1},
Pages = {219338},
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 = {0677164203},
MRNUMBER = {85k:58005},
url = {http://www.ams.org/mathscinetgetitem?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 = {46574660},
Year = {1981},
MRNUMBER = {82h:53074},
url = {http://www.ams.org/mathscinetgetitem?mr=82h:53074},
Key = {fds243388}
}
%% Papers Accepted
@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 GelfandGelfand
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}
}
%% Preprints
@article{fds225242,
Author = {R.L. Bryant and Feng Xu},
Title = {Laplacian flow for closed G_{2}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}
}
