Publications of Robert Bryant


  1. with Bryant, RL; Chern, SS; Gardner, RB; Goldschmidt, HL; Griffiths, PA, Exterior Differential Systems (December, 2011), pp. 475 pages, SPRINGER, ISBN 1461397162
  2. 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
  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
  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.)
  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
  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
  7. 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

Papers Published

  1. Bryant, R; Buckmire, R; Khadjavi, L; Lind, D, The origins of spectra, an organization for LGBT mathematicians, Notices of the American Mathematical Society, vol. 66 no. 6 (June, 2019), pp. 875-882
  2. 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, Elsevier BV
  3. Bryant, RL, On the convex Pfaff-Darboux Theorem of Ekeland and Nirenberg (December, 2015)
  4. Bryant, RL, On the conformal volume of 2-tori (July, 2015)
  5. Bryant, RL, S.-S. Chern's study of almost-complex structures on the six-sphere (May, 2014)
  6. Bryant, RL, Notes on exterior differential systems (May, 2014)
  7. Bryant, RL; Eastwood, MG; Gover, AR; Neusser, K, Some differential complexes within and beyond parabolic geometry (March, 2012)
  8. Bryant, R; Xu, F, Laplacian Flow for Closed $G_2$-Structures: Short Time Behavior (January, 2011)
  9. Bryant, RL, Nonembedding and nonextension results in special holonomy, in The Many Facets of Geometry, edited by Garcia-Prada, O; Bourguignon, JP; Salamon, S (Fall, 2010), pp. 346-367, Oxford University Press, Oxford, ISBN 9780199534920
  10. with Bryant, RL; Dunajski, M; Eastwood, M, Metrisability of two-dimensional projective structures, vol. 83 no. 3 (2009), pp. 465-500, International Press of Boston, ISSN 0022-040X
  11. Bryant, RL, Commentary, Bulletin of the American Mathematical Society, vol. 46 no. 2 (April, 2009), pp. 177-178, American Mathematical Society (AMS), ISSN 0273-0979
  12. 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, Springer Nature America, Inc
  13. Bryant, RL, Gradient Kähler Ricci solitons, in Géométrie différentielle, physique mathématique, mathématiques et société. I., Astérisque, Astérisque, vol. 321 no. 321 (Spring, 2008), pp. 51-97, Soc. Math. France, ISBN 978-285629-258-7
  14. BRYANT, RL, Conformal geometry and 3-plane fields on 6-manifolds, in Developments of Cartan Geometry and Related Mathematical Problems, RIMS Symposium Proceedings, Rims Kokyuroku, vol. 1502 (Developments of Cartan Geometry an (July, 2006), pp. 1-15, Kyoto University
  15. Bryant, RL, On the geometry of almost complex 6-manifolds, Asian Journal of Mathematics, vol. 10 no. 3 (January, 2006), pp. 561-605, International Press of Boston
  16. 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, Springer Nature
  17. Bryant, R; Freed, D, Shiing-Shen Chern, Physics Today, vol. 59 no. 1 (January, 2006), pp. 70-72, AIP Publishing
  18. Bryant, RL, Second order families of special Lagrangian 3-folds, in Perspectives in Riemannian Geometry, CRM Proceedings and Lecture Notes, edited by Apostolov, V; Dancer, A; Hitchin, N; Wang, M, Perspectives in Riemannian Geometry, vol. 40 (January, 2006), pp. 63-98, AMER MATHEMATICAL SOC, ISBN 0-8218-3852-0
  19. 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, edited by Jensen, GR; Krantz, SG, Surveys on Discrete and Computational Geometry: Twenty Years Later, vol. 395 (January, 2006), pp. 29-38, AMER MATHEMATICAL SOC, ISBN 0-8218-3603-X
  20. 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
  21. 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
  22. 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.)
  23. Bryant, RL, Real hypersurfaces in unimodular complex surfaces (July, 2004)
  24. with Bryant, R; Edelsbrunner, H; Koehl, P; Levitt, M, The area derivative of a space-filling diagram, Discrete & Computational Geometry, vol. 32 no. 3 (January, 2004), pp. 293-308, Springer Nature (ISSN: 0179-5376.)
  25. Bryant, RL, Some remarks on Finsler manifolds with constant flag curvature, Houston Journal of Mathematics, vol. 28 no. 2 (January, 2002), pp. 221-262, UNIV HOUSTON
  26. 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
  27. Bryant, RL, On surfaces with prescribed shape operator, Results Math. 40 (2001), No. 1 4, 88 121, vol. 40 no. 1-4 (October, 2001), pp. 88-121, Springer Nature (Dedicated to Shiing-Shen Chern on his 90th birthday.)
  28. Bryant, RL, Bochner-kähler metrics, Journal of the American Mathematical Society, vol. 14 no. 3 (July, 2001), pp. 623-715
  29. Bryant, RL, Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces (March, 2001)
  30. Bryant, R, Recent advances in the theory of holonomy, Astérisque, vol. 266 no. 5 (December, 2000), pp. 351-374, Centre National de la Recherche Scientifique (Exposé No. 861.)
  31. Bryant, RL, Harmonic morphisms with fibers of dimension one, Communications in Analysis and Geometry, vol. 8 no. 2 (January, 2000), pp. 219-265, International Press of Boston
  32. 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).)
  33. 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
  34. 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
  35. Bryant, RL, Some examples of special Lagrangian Tori, Advances in Theoretical and Mathematical Physics, vol. 3 no. 1 (January, 1999), pp. 83-90, International Press of Boston
  36. with Bryant, RL; Sharpe, E, D-branes and Spinc structures, Physics Letters B, vol. 450 no. 4 (January, 1999), pp. 353-357, Elsevier BV
  37. 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
  38. Bryant, RL, Projectively flat finsler 2-spheres of constant curvature, Selecta Mathematica, vol. 3 no. 2 (January, 1997), pp. 161-203, Springer Nature
  39. 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
  40. 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
  41. 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
  42. with Bryant, R; Griffiths, P; Hsu, L, Hyperbolic exterior differential systems and their conservation laws, part II, Selecta Mathematica, vol. 1 no. 2 (September, 1995), pp. 265-323, Springer Nature
  43. with Bryant, RL; Griffiths, PA, Characteristic cohomology of differential systems. I. General theory, Journal of the American Mathematical Society, vol. 8 no. 3 (September, 1995), pp. 507-507, American Mathematical Society (AMS)
  44. with Bryant, R; Griffiths, P; Hsu, L, Hyperbolic exterior differential systems and their conservation laws, part I, Selecta Mathematica, vol. 1 no. 1 (March, 1995), pp. 21-112, Springer Nature
  45. with Bryant, RL; Griffiths, PA, Characteristic cohomology of differential systems II: Conservation laws for a class of parabolic equations, Duke Mathematical Journal, vol. 78 no. 3 (January, 1995), pp. 531-676, Duke University Press
  46. 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 Yau, ST, Geometry, Topology & Physics, vol. 4 (January, 1995), pp. 1-76, INTERNATIONAL PRESS INC BOSTON, ISBN 1-57146-024-1
  47. 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
  48. 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
  49. with Bryant, RL; Hsu, L, Rigidity of integral curves of rank 2 distributions, Inventiones Mathematicae, vol. 114 no. 1 (December, 1993), pp. 435-461, Springer Nature, ISSN 0020-9910
  50. Bryant, RL, Some remarks on the geometry of austere manifolds, Boletim Da Sociedade Brasileira De Matem�Tica, vol. 21 no. 2 (September, 1991), pp. 133-157, Springer Nature
  51. 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
  52. with Bryant, R; Harvey, R, Submanifolds in hyper-Kähler geometry, Journal of the American Mathematical Society, vol. 2 no. 1 (January, 1989), pp. 1-31, American Mathematical Society (AMS)
  53. with Bryant, RL; Salamon, SM, On the construction of some complete metrics with exceptional holonomy, Duke Mathematical Journal, vol. 58 no. 3 (January, 1989), pp. 829-850, Duke University Press
  54. 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
  55. 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
  56. Bryant, RL, Metrics with exceptional holonomy, Ann. of Math. (2), vol. 126 no. 3 (1987), pp. 525-576
  57. 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
  58. 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
  59. 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
  60. with Bryant, R; Griffiths, P, Reduction for Constrained Variational Problems and � κ 2 2 ds, American Journal of Mathematics, vol. 108 no. 3 (June, 1986), pp. 525-525, JSTOR
  61. Bryant, RL, Minimal surfaces of constant curvature in sn, Transactions of the American Mathematical Society, vol. 290 no. 1 (January, 1985), pp. 259-271, American Mathematical Society (AMS)
  62. Bryant, RL, Lie groups and twlstor spaces, Duke Mathematical Journal, vol. 52 no. 1 (January, 1985), pp. 223-261, Duke University Press
  63. 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
  64. Bryant, RL, A duality theorem for willmore surfaces, Journal of Differential Geometry, vol. 20 no. 1 (January, 1984), pp. 23-53, International Press of Boston
  65. with Bryant, RL; Griffiths, PA; Yang, D, Characteristics and existence of isometric embeddings, Duke Mathematical Journal, vol. 50 no. 4 (January, 1983), pp. 893-994, Duke University Press
  66. with Berger, E; Bryant, R; Griffiths, P, The Gauss equations and rigidity of isometric embeddings, Duke Mathematical Journal, vol. 50 no. 3 (January, 1983), pp. 803-892, Duke University Press
  67. 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
  68. Bryant, RL, Holomorphic curves in lorentzian cr-manifolds, Transactions of the American Mathematical Society, vol. 272 no. 1 (January, 1982), pp. 203-221, American Mathematical Society (AMS)
  69. Bryant, RL, Submanifolds and special structures on the octonians, Journal of Differential Geometry, vol. 17 no. 2 (January, 1982), pp. 185-232, International Press of Boston
  70. Bryant, RL, Conformal and minimal immersions of compact surfaces into the 4-sphere, Journal of Differential Geometry, vol. 17 no. 3 (January, 1982), pp. 455-473, International Press of Boston
  71. 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
  72. 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

Papers Accepted

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


  1. R.L. Bryant and Feng Xu, Laplacian flow for closed G2-structures: short time behavior (January, 2011)