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Publications of Robert Bryant    :chronological  alphabetical  combined  bibtex listing:

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Books

  1. with Bryant, RL; Chern, SS; Gardner, RB; Goldschmidt, HL; Griffiths, PA, Exterior Differential Systems (December, 2011), pp. 475 pages, Springer, ISBN 1461397162 [MR92h:58007]  [abs] [author's comments]
  2. Gu, C; Berger, M; Bryant, RL, Differential Geometry and Differential Equations Proceedings of a Symposium, held in Shanghai, June 21 - July 6, 1985 (November, 2006), pp. 246 pages, Springer, ISBN 3540478833  [abs]
  3. with David Bao, S.-S. Chern, Zhongmin Shen, eds., A Sampler of Riemann-Finsler Geometry, Mathematical Sciences Research Institute Publications, edited by Bao, D; Bryant, RL; Chern, S-S; Shen, Z, vol. 50 (November, 2004), pp. 363 pages, Cambridge University Press, ISBN 0521831814 [MR2132655(2005j:53003)]  [abs]
  4. with Bryant, R; Griffiths, P; Grossman, D, Exterior Differential Systems and Euler-Lagrange Partial Differential Equations, Chicago Lectures in Mathematics (July, 2003), pp. 213 pages, University of Chicago Press, ISBN 0226077934 (vii+213 pages, ISBN: 0-226-07794-2.) [MR1985469], [math.DG/0207039]  [abs] [author's comments]
  5. Selected works of Phillip A. Griffiths with commentary. Part 4. Differential systems., edited by R. L. Bryant and David R. Morrison (2003), American Mathematical Society, Providence, RI; International Press, Somerville, MA [MR2005e:01025d]
  6. with Victor Guillemin, Sigurdur Helgason, and R. O. Wells, Jr. (eds.), Integral Geometry, edited by Bryant, R; Guillemin, V; Helgason, S; Wells, RO, vol. 63 (1987), pp. 350 pages, American Mathematical Society, ISBN 0-8218-5071-7 [MR87j:53003]  [abs]
  7. Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces, Annals of Mathematics Studies (to appear) [math.DG/0006186]  [author's comments]
  8. with Marcel Berger and Chao Hao Gu (eds.), Differential Geometry and Differential Equations, Proceedings of the sixth symposium held at Fudan University, Shanghai, June 21--July 6, 1985, pp. xii+243, 1987, Springer-Verlag, Berlin [MR88b:53002]

Papers Published

  1. Bryant, RL, Non-Embedding and Non-Extension Results in Special Holonomy, in The Many Facets of Geometry: A Tribute to Nigel Hitchin, edited by Garcia-Prada, O; Bourguignon, JP; Salamon, S (Fall, 2010), pp. 346-367, Oxford University Press, Oxford, ISBN 0199534926 [MR2681703], [doi]  [abs]
  2. Bryant, RL, Commentary, Bulletin of the American Mathematical Society, vol. 46 no. 2 (2009), pp. 177-178, ISSN 0273-0979 [doi]
  3. with Dunajski, M; Eastwood, M; Bryant, RL, Metrisability of two-dimensional projective structures, Journal of Differential Geometry, vol. 83 no. 3 (2009), pp. 465-499, ISSN 0022-040X [MR2581355], [arXiv:0801.0300v1 [math.DG]]  [abs]
  4. Gradient Kähler Ricci Solitons, in Géométrie différentielle, physique mathématique, mathématiques et société. I., Astérisque, vol. 321 (Spring, 2008), pp. 51--97, ISBN 978-285629-258-7 [MR2010i:53138], [math.DG/0407453]  [abs]
  5. with Manno, G; Matveev, V; Bryant, RL, A solution of a problem of Sophus Lie: Normal forms of 2-dimensional metrics admitting two projective vector fields, Mathematische Annalen, vol. 340 no. 2 (Spring, 2008), pp. 437-463 [3592]  [abs]
  6. Bryant, RL, Gradient Kähler Ricci solitons, Asterisque no. 321 (2008), pp. 51-97, Soc. Math. France, ISSN 0303-1179  [abs]
  7. Bryant, RL, On the geometry of almost complex 6-manifolds, The Asian Journal of Mathematics, vol. 10 no. 3 (September, 2006), pp. 561-606 [math.DG/0508428]  [abs]
  8. BRYANT, RL, Conformal geometry and 3-plane fields on 6-manifolds, in Developments of Cartan Geometry and Related Mathematical Problems, RIMS Symposium Proceedings, vol. 1502 (Developments of Cartan Geometry an (July, 2006), pp. 1-15, Kyoto University [math.DG/0511110]  [abs] [author's comments]
  9. Bryant, RL, SO(n)-invariant special Lagrangian submanifolds of C^{n+1} with fixed loci, Chinese Annals of Mathematics, Series B, vol. 27 no. 1 (January, 2006), pp. 95-112 [MR2209954], [math.DG/0402201]  [abs]
  10. Bryant, R; Freed, D, Shiing-Shen Chern - Obituary, Physics today, vol. 59 no. 1 (January, 2006), pp. 70-72 [doi]
  11. Bryant, RL, Second order families of special Lagrangian 3-folds, in Perspectives in Riemannian Geometry, CRM Proceedings and Lecture Notes, edited by Vestislav Apostolov, Andrew Dancer, Nigel Hitchin, and McKenzie Wang, Perspectives in Riemannian Geometry, vol. 40 (2006), pp. 63-98, American Mathematical Society, ISBN 0-8218-3852-0 [math.DG/0007128]  [abs]
  12. Bryant, RL, Geometry of manifolds with special holonomy: "100 years of holonomy", in 150 years of mathematics at Washington University in St. Louis, Contemporary Mathematics, Contemporary Mathematics, vol. 395 (2006), pp. 29-38, AMS, ISBN 0-8218-3603-X [MR2206889]  [author's comments]
  13. Bryant, R, Geodesically reversible Finsler 2-spheres of constant curvature, in Inspired by S. S. Chern---A Memorial Volume in Honor of a Great Mathematician, Nankai Tracts in Mathematics, edited by Griffiths, PA, vol. 11 (Winter, 2006), pp. 95-111, World Scientific Publishers [math.DG/0407514]  [abs]
  14. Bryant, R, Some remarks on G2-structures, in Proceedings of Gökova Geometry-Topology Conference 2005, edited by Akbulut, S; Onder, T; Stern, R (2006), pp. 75-109, International Press, ISBN 1-57146-152-3 [math.DG/0305124]  [abs]
  15. Bryant, R, Holonomy and Special Geometries, in Dirac Operators: Yesterday and Today, Conference Proceedings and Lecture Notes in Geometry and Topology, edited by Bourguinon, JP; Branson, T; Chamseddine, A; Hijazi, O; Stanton, R (2005), pp. 71-90, International Press, ISBN 1-57146-175-2 (Proceedings of the Summer School and Workshop at CAMS-AUB, Lebanon, August 27 -- September 7, 2001.) [MR2205367]
  16. with Bryant, R; Edelsbrunner, H; Koehl, P; Levitt, M, The area derivative of a space-filling diagram, Discrete and Computanional Geometry, vol. 32 no. 3 (2004), pp. 293-308 (ISSN: 0179-5376.) [MR2005k:92077], [doi]  [abs]
  17. Levi-flat minimal hypersurfaces in two-dimensional complex space forms, in Lie groups, geometric structures and differential equations---one hundred years after Sophus Lie (Kyoto/Nara, 1999), Adv. Stud. Pure Math., vol. 37 (2002), pp. 1--44, Math. Soc. Japan [MR1980895], [math.DG/9909159]  [abs]
  18. Bryant, RL, Some remarks on Finsler manifolds with constant flag curvature, Houston Journal of Mathematics, vol. 28 no. 2 (2002), pp. 221-262 [MR2003h:53102], [math.DG/0107228]  [abs]
  19. Bryant, RL, On surfaces with prescribed shape operator, Results in Mathematics, vol. 40 no. 1--4 (2001), pp. 88-121 (Dedicated to Shiing-Shen Chern on his 90th birthday.) [MR2002i:53010], [math.DG/0107083]  [abs] [author's comments]
  20. Bryant, RL, Bochner-Kähler metrics, Journal of the AMS, vol. 14 no. 3 (2001), pp. 623-715 [MR2002i:53096], [math.DG/0003099]  [abs]
  21. Bryant, RL, Recent advances in the theory of holonomy, Asterisque, vol. 266 no. 5 (2000), pp. 351-374, Centre National de la Recherche Scientifique (Exposé No. 861.) [MR2001h:53067], [math.DG/9910059], [html]  [author's comments]
  22. Bryant, RL, Harmonic morphisms with fibers of dimension one, Communications in Analysis and Geometry, vol. 8 no. 2 (2000), pp. 219-265 [MR2001i:53101], [dg-ga/9701002]  [abs]
  23. Bryant, RL, Calibrated embeddings in the special Lagrangian and coassociative cases, Annals of Global Analysis and Geometry, vol. 18 no. 3-4 (2000), pp. 405-435 (Special issue in memory of Alfred Gray (1939--1998).) [MR2002j:53063], [math.DG/9912246]  [abs]
  24. Bryant, RL, Calibrated Embeddings in the Special Lagrangian and Coassociative Cases, Annals of Global Analysis and Geometry, vol. 18 no. 3-4 (2000), pp. 405-435  [abs]
  25. Bryant, R, Élie Cartan and geometric duality, in Journées Élie Cartan 1998 et 1999, Journées Élie Cartan 1998 et 1999, vol. 16 (2000), pp. 5-20, Institut Élie Cartan [pdf]  [author's comments]
  26. Bryant, R, Pseudo-Reimannian metrics with parallel spinor fields and vanishing Ricci tensor, in Global analysis and harmonic analysis (Marseille-Luminy, 1999), Séminaires & Congrès, edited by Bourguinon, JP; Branson, T; Hijazi, O, vol. 4 (2000), pp. 53-94, Société Mathématique de France, ISBN 2-85629-094-9 [MR2002h:53082], [math.DG/0004073]  [abs]
  27. Bryant, RL, Some examples of special Lagrangian tori, Adv. Theor. Math. Phys., vol. 3 no. 1 (1999), pp. 83-90 [MR2000f:32033], [math.DG/9902076]  [abs]
  28. with Sharpe, E; Bryant, RL, D-branes and Spin^c-structures, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, vol. 450 no. 4 (1999), pp. 353-357 [MR2000c:53054], [hep-th/98l2084]  [abs]
  29. Russell, Thomas and Farris, Frank, Integrability, Gorman systems, and the Lie bracket structure of the real line (with an appendix by –––), J. Math. Econom., vol. 29 no. 2 (1998), pp. 183–209 [MR99f:90029]
  30. Bryant, RL, Projectively flat Finsler 2-spheres of constant curvature, Selecta Math. (N.S.), vol. 3 no. 2 (1997), pp. 161-203 [MR98i:53101], [dg-ga/9611010]  [author's comments]
  31. Finsler structures on the 2-sphere satisfying K=1, in Finsler geometry (Seattle, WA, 1995), Contemporary Mathematics, edited by David Bao, Shiing-shen Chern and Zhongmin Shen, vol. 196 (1996), pp. 27–41, Amer. Math. Soc., Providence, RI [MR97e:53128], [dvi]  [author's comments]
  32. Bryant, R, On extremals with prescribed Lagrangian densities, in Manifolds and geometry (Pisa, 1993), Symposia Mathematica, edited by Bartolomeis, P; Tricerri, F; Vesentini, E, vol. 36 (1996), pp. 86-111, Cambridge University Press, ISBN 0-521-56216-3 [MR99a:58043], [dg-ga/9406001]  [abs] [author's comments]
  33. Bryant, R, Classical, exceptional, and exotic holonomies: a status report, in Actes de la Table Ronde de Géométrie Différentielle, Sémin. Congr., edited by Besse, A, vol. 1 (1996), pp. 93-165, Société Mathématique de France, ISBN 2-85629-047-7 [MR98c:53037], [dvi]  [abs]
  34. with Griffiths, PA; Hsu, L; Bryant, RL, Hyperbolic exterior differential systems and their conservation laws, Part II, Selecta Math. (N.S.), vol. 1 no. 2 (1995), pp. 265-323 [MR97d:580009], [dvi]
  35. with Griffiths, PA; Hsu, L; Bryant, RL, Hyperbolic exterior differential systems and their conservation laws, Part I, Selecta Math. (N.S.), vol. 1 no. 1 (1995), pp. 21-112 [MR97d:580008], [dvi]
  36. with Bryant, RL; Griffiths, PA, Characteristic cohomology of differential systems, II: Conservation laws for a class of parabolic equations, Duke Math. Journal, vol. 78 no. 3 (1995), pp. 531-676 [MR96d:58158], [dvi]  [author's comments]
  37. with Griffiths, PA; Bryant, RL, Characteristic cohomology of differential systems, I: General theory, J. Amer. Math. Soc., vol. 8 no. 3 (1995), pp. 507-596 [MR96c:58183], [dvi]  [author's comments]
  38. with BRYANT, R; GRIFFITHS, P; HSU, L, Toward a geometry of differential equations, in Geometry, Topology, & Physics, Conf. Proc. Lecture Notes Geom. Topology, edited by S.-T. Yau, GEOMETRY, TOPOLOGY & PHYSICS, vol. 4 (1995), pp. 1-76, Internat. Press, Cambridge, MA, ISBN 1-57146-024-1 [MR97b:58005], [dvi]
  39. with Bryant, R; Gardner, RB, Control Structures, in Geometry in nonlinear control and differential inclusions (Warsaw, 1993), Banach Center Publications, edited by Jakubczyk, B; Respondek, W; Rzezuchowski, T, vol. 12 (1995), pp. 111-121, Polish Academy of Sciences [MR96h:93024], [dvi]
  40. Bryant, R, An introduction to Lie groups and symplectic geometry, in Geometry and quantum field theory (Park City, UT, 1991), IAS/Park City Mathematics, edited by Freed, D; Uhlenbeck, K, vol. 1 (1995), pp. 5-181, American Mathematical Society, ISBN 0-8218-0400-6 [MR96i:58002]  [abs] [author's comments]
  41. Bryant, RL; Hsu, L, Rigidity of integral curves of rank 2 distributions, Inventiones mathematicae, vol. 114 no. 1 (1993), pp. 435-461, ISSN 0020-9910 [doi]
  42. Bryant, RL, Some remarks on the geometry of austere manifolds, Bol. Soc. Brasil. Mat. (N.S.), vol. 21 no. 2 (1991), pp. 133-157 [MR92k:53112], [dvi]  [author's comments]
  43. Bryant, R, Two exotic holonomies in dimension four, path geometries, and twistor theory, in Complex geometry and Lie theory (Sundance, UT, 1989), Proc. Sympos. Pure Math., edited by Carlson, J; Clemens, H; Morrison, D, vol. 53 (1991), pp. 33-88, American Mathematical Society, ISBN 0-8218-1492-3 [MR93e:53030], [dvi]  [author's comments]
  44. with Harvey, FR; Bryant, RL, Submanifolds in hyper-Kähler geometry, J. Amer. Math. Soc., vol. 2 no. 1 (1989), pp. 1-31 [MR89m:53090]  [author's comments]
  45. with Salamon, S; Bryant, RL, On the construction of some complete metrics with exceptional holonomy, Duke Math. J., vol. 58 no. 3 (1989), pp. 829-850 [MR90i:53055]  [author's comments]
  46. Bryant, R, Surfaces in conformal geometry, in The mathematical heritage of Hermann Weyl (Durham, NC, 1987), Proc. Sympos. Pure Math., edited by Wells, RO, vol. 48 (1988), pp. 227-240, American Mathematical Society, ISBN 0-8218-1482-6 [MR89m:53102]  [abs] [author's comments]
  47. Bryant, R, Surfaces of mean curvature one in hyperbolic space, in Théorie des variétés minimales et applications (Palaiseau, 1983–1984), Astérisque, vol. 154-155 (1988), pp. 321-347, Société Mathématique de France [MR955072]  [author's comments]
  48. Bryant, RL, Metrics with exceptional holonomy, Ann. of Math. (2), vol. 126 no. 3 (1987), pp. 525-576 [MR89b:53084]  [author's comments]
  49. Bryant, R, On notions of equivalence of variational problems with one independent variable, in Differential geometry: the interface between pure and applied mathematics (San Antonio, Tex., 1986), Contemporary Mathematics, edited by Luksic, M; Martin, C; Shadwick, W, vol. 68 (1987), pp. 65-76, American Mathematical Society, ISBN 0-8218-5075-X [MR89f:58037]  [author's comments]
  50. Bryant, R, A survey of Riemannian metrics with special holonomy groups, in Proceedings of the International Congress of Mathematicians. Vol. 1, 2. (Berkeley, Calif., 1986), edited by Gleason, A (1987), pp. 505-514, American Mathematical Society, ISBN 0-8218-0110-4 [MR89f:53068]  [author's comments]
  51. Bryant, R, Minimal Lagrangian submanifolds of Kähler-Einstein manifolds, in Differential geometry and differential equations (Shanghai, 1985), Lecture Notes in Math., edited by Gu, C; Berger, M; Bryant, RL, vol. 1255 (1987), pp. 1-12, Springer-Verlag, ISBN 3-540-17849-X [MR88j:53061]  [author's comments]
  52. with Griffiths, PA; Bryant, RL, Reduction for constrained variational problems and $\int{1\over 2}k\sp 2\,ds$, Amer. J. Math., vol. 108 no. 3 (1986), pp. 525-570 [MR88a:58044]  [author's comments]
  53. Bryant, RL, Minimal surfaces of constant curvature in S^n, Trans. Amer. Math. Soc., vol. 290 no. 1 (1985), pp. 259-271 [MR87c:53110]  [author's comments]
  54. Bryant, RL, Lie groups and twistor spaces, Duke Math. J., vol. 52 no. 1 (1985), pp. 223-261 [MR87d:58047]  [author's comments]
  55. Bryant, R, Metrics with holonomy G2 or Spin(7), in Workshop Bonn 1984 (Bonn, 1984), Lecture Notes in Math., edited by Hirzebruch, F; Schwermer, J; Suter, S, vol. 1111 (1985), pp. 269-277, Springer [MR87a:53082]  [author's comments]
  56. Bryant, RL, A duality theorem for Willmore surfaces, J. Differential Geom., vol. 20 no. 1 (1984), pp. 23-53 [MR86j:58029]  [author's comments]
  57. with Griffiths, P; Yang, D, Characteristics and existence of isometric embeddings, Duke Math. J., vol. 50 no. 4 (1983), pp. 893-994 [MR85d:53027]  [author's comments]
  58. with Berger, E; Griffiths, P, The Gauss equations and rigidity of isometric embeddings, Duke Math. J., vol. 50 no. 3 (1983), pp. 803-892 [MR85k:53056]  [author's comments]
  59. with Bryant, R; Griffiths, PA, Some observations on the infinitesimal period relations for regular threefolds with trivial canonical bundle, in Arithmetic and geometry, Vol. II, Progress in Mathematics, edited by Artin, M; Tate, J, vol. 36 (1983), pp. 77-102, Birkhäuser Boston, ISBN 3-7643-3133-X [MR86a:32044]  [author's comments]
  60. Bryant, RL, Holomorphic curves in Lorentzian CR-manifolds, Trans. Amer. Math. Soc., vol. 272 no. 1 (1982), pp. 203-221 [MR83i:32029]  [abs]
  61. Bryant, RL, Submanifolds and special structures on the octonians, J. Differential Geom., vol. 17 no. 2 (1982), pp. 185-232 [MR84h:53091]  [abs]
  62. Bryant, RL, Conformal and minimal immersions of compact surfaces into the 4-sphere, J. Differential Geom., vol. 17 no. 3 (1982), pp. 455-473 [MR84a:53062]  [author's comments]
  63. with Bryant, R; Chern, SS; Griffiths, PA, Exterior Differential Systems, in Proceedings of the 1980 Beijing Symposium on Differential Geometry and Differential Equations (Beijing, 1980), edited by Chern, SS; Wu, WT, vol. 1 (1982), pp. 219-338, Science Press; Gordon & Breach Science Publishers, ISBN 0-677-16420-3 [MR85k:58005]  [author's comments]
  64. with Berger, E; Griffiths, P, Some isometric embedding and rigidity results for Riemannian manifolds, Proc. Nat. Acad. Sci. U.S.A., vol. 78 no. 8 (1981), pp. 4657-4660 [MR82h:53074]  [author's comments]

Papers Accepted

  1. with Michael G. Eastwood, A. Rod. Gover, Katharina Neusser, Some differential complexes within and beyond parabolic geometry (December, 2011) [arXiv:1112.2142v2]  [abs] [author's comments]

Preprints

  1. R. Bryant, On the convex Pfaff-Darboux Theorem of Ekeland and Nirenberg (December 22, 2015) [arXiv:1512.07100]  [abs]
  2. R. Bryant, On the conformal volume of 2-tori (July 6, 2015) [arXiv:1507.01485]  [abs]
  3. R.L. Bryant, Notes on Exterior Differential Systems (May, 2014) [arXiv:1405.3116]  [abs] [author's comments]
  4. R.L. Bryant, S.-s. Chern's study of almost-complex structures on the six-sphere (May, 2014) [arXiv:1405.3405]  [abs]
  5. R.L. Bryant and Feng Xu, Laplacian flow for closed G2-structures: short time behavior (January, 2011) [arXiv:1101.2004]  [abs]
  6. R.L. Bryant, Real hypersurfaces in unimodular complex surfaces (July 27, 2004) [math.DG/0407472]  [abs]

 

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