Publications of Robert Bryant

Books

  1. 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
  2. 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
  3. Bryant, RL, Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces (March, 2001)
  4. 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
  5. with Bryant, RL; Griffiths, PA; Grossman, DA, 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.)
  6. 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
  7. with 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
  8. with Bryant, RL; Chern, SS; Gardner, RB; Goldschmidt, HL; Griffiths, PA, Exterior Differential Systems (December, 2011), pp. 475 pages, Springer, ISBN 1461397162

Papers Published

  1. 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
  2. Bryant, RL, Holomorphic curves in Lorentzian CR-manifolds, Trans. Amer. Math. Soc., vol. 272 no. 1 (1982), pp. 203-221
  3. Bryant, RL, Submanifolds and special structures on the octonians, J. Differential Geom., vol. 17 no. 2 (1982), pp. 185-232
  4. Bryant, RL, Conformal and minimal immersions of compact surfaces into the 4-sphere, J. Differential Geom., vol. 17 no. 3 (1982), pp. 455-473
  5. 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
  6. with Griffiths, P; Yang, D, Characteristics and existence of isometric embeddings, Duke Math. J., vol. 50 no. 4 (1983), pp. 893-994
  7. with Berger, E; Griffiths, P, The Gauss equations and rigidity of isometric embeddings, Duke Math. J., vol. 50 no. 3 (1983), pp. 803-892
  8. 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
  9. Bryant, RL, A duality theorem for Willmore surfaces, J. Differential Geom., vol. 20 no. 1 (1984), pp. 23-53
  10. Bryant, RL, Minimal surfaces of constant curvature in S^n, Trans. Amer. Math. Soc., vol. 290 no. 1 (1985), pp. 259-271
  11. Bryant, RL, Lie groups and twistor spaces, Duke Math. J., vol. 52 no. 1 (1985), pp. 223-261
  12. 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
  13. 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
  14. Bryant, RL, Metrics with exceptional holonomy, Ann. of Math. (2), vol. 126 no. 3 (1987), pp. 525-576
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. with Harvey, FR; Bryant, RL, Submanifolds in hyper-Kähler geometry, J. Amer. Math. Soc., vol. 2 no. 1 (1989), pp. 1-31
  21. 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
  22. Bryant, RL, Some remarks on the geometry of austere manifolds, Bol. Soc. Brasil. Mat. (N.S.), vol. 21 no. 2 (1991), pp. 133-157
  23. 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
  24. with 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
  25. 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
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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
  31. with Bryant, RL; Griffiths, PA, Characteristic cohomology of differential systems. I. General theory, The Journal of the American Mathematical Society, vol. 8 no. 3 (1995), pp. 507-507
  32. Bryant, RL, 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
  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
  34. 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
  35. Bryant, RL, Projectively flat Finsler 2-spheres of constant curvature, Selecta Math. (N.S.), vol. 3 no. 2 (1997), pp. 161-203
  36. 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
  37. Bryant, RL, Some examples of special Lagrangian tori, Adv. Theor. Math. Phys., vol. 3 no. 1 (1999), pp. 83-90
  38. 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
  39. 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.)
  40. Bryant, RL, Harmonic morphisms with fibers of dimension one, Communications in Analysis and Geometry, vol. 8 no. 2 (2000), pp. 219-265
  41. 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).)
  42. 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
  43. Bryant, RL, Pseudo-Riemannian 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
  44. Bryant, RL, On surfaces with prescribed shape operator, Results Math. 40 (2001), no. 1-4, 88--121, vol. 40 no. 1--4 (2001), pp. 88-121 (Dedicated to Shiing-Shen Chern on his 90th birthday.)
  45. Bryant, RL, Bochner-Kähler metrics, Journal of the AMS, vol. 14 no. 3 (2001), pp. 623-715
  46. Bryant, RL, Some remarks on Finsler manifolds with constant flag curvature, Houston Journal of Mathematics, vol. 28 no. 2 (2002), pp. 221-262
  47. 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
  48. 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.)
  49. 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.)
  50. 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, CRM Proceedings and Lecture Notes, edited by Vestislav Apostolov, Andrew Dancer, Nigel Hitchin, and McKenzie Wang, vol. 40 (2006), American Mathematical Society, vol. 40 (2006), pp. 63-98, American Mathematical Society, ISBN 0-8218-3852-0
  51. 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
  52. Bryant, RL, 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
  53. Bryant, RL, Some remarks on G_2-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
  54. 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
  55. Bryant, R; Freed, D, Shiing-Shen Chern - Obituary, Physics today, vol. 59 no. 1 (January, 2006), pp. 70-72
  56. 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
  57. Bryant, RL, On the geometry of almost complex 6-manifolds, The Asian Journal of Mathematics, vol. 10 no. 3 (September, 2006), pp. 561-606
  58. with Bryant, RL; Manno, G; Matveev, VS, A solution of a problem of Sophus Lie: Normal forms of two-dimensional metrics admitting two projective vector fields, Mathematische Annalen, vol. 340 no. 2 (Spring, 2008), pp. 437-463
  59. Bryant, RL, Gradient Kähler Ricci solitons, in Géométrie différentielle, physique mathématique, mathématiques et société. I., Astérisque, Asterisque, vol. 321 no. 321 (Spring, 2008), pp. 51-97, Soc. Math. France, ISBN 978-285629-258-7
  60. Bryant, RL, Commentary, Bulletin of the American Mathematical Society, vol. 46 no. 2 (2009), pp. 177-178, ISSN 0273-0979
  61. with Bryant, RL; Dunajski, M; Eastwood, M, Metrisability of two-dimensional projective structures, vol. 83 no. 3 (2009), pp. 465-499, ISSN 0022-040X
  62. Bryant, RL, Nonembedding and nonextension 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
  63. Bryant, R; Xu, F, Laplacian Flow for Closed $G_2$-Structures: Short Time Behavior (January, 2011)
  64. Bryant, RL; Eastwood, MG; Gover, AR; Neusser, K, Some differential complexes within and beyond parabolic geometry (March, 2012)
  65. Bryant, RL; Huang, L; Mo, X, On Finsler surfaces of constant flag curvature with a Killing field, Journal of Geometry and Physics, vol. 116 (June, 2017), pp. 345-357

Papers Accepted

  1. with Michael G. Eastwood, A. Rod. Gover, Katharina Neusser, Some differential complexes within and beyond parabolic geometry (December, 2011)

Preprints

  1. Bryant, RL, Real hypersurfaces in unimodular complex surfaces (July 27, 2004)
  2. R.L. Bryant and Feng Xu, Laplacian flow for closed G2-structures: short time behavior (January, 2011)
  3. Bryant, RL, Notes on exterior differential systems (May, 2014)
  4. Bryant, RL, S.-S. Chern's study of almost-complex structures on the six-sphere (May, 2014)
  5. Bryant, RL, On the conformal volume of 2-tori (July 6, 2015)
  6. Bryant, RL, On the convex Pfaff-Darboux Theorem of Ekeland and Nirenberg (December 22, 2015)