Publications of Robert Bryant

Books

  1. with Bryant, RL; Chern, SS; Gardner, RB; Goldschmidt, HL; Griffiths, PA, Exterior Differential Systems (December, 2011), pp. 475 pages, Springer, ISBN 9781461397168
  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 9783540478836
  3. with Bao, DD-W, 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 9780521831819
  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 9780226077932 (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, The generality of closed G_2 solitons, edited by Cheng, S-Y; Lima-Filho, P; Yau, SS-T; Yau, S-T, Pure and Applied Mathematics Quarterly, vol. 19 no. 6 (January, 2024), pp. 2827-2840, International Press
  2. Bryant, R; Cheeger, J; Lima-Filho, P; Rosenberg, J; White, B, The mathematical work of H. Blaine Lawson, Jr., Pure and Applied Mathematics Quarterly, vol. 19 no. 6 (January, 2024), pp. 2627-2662, International Press
  3. Bryant, R; Cheeger, J; Griffiths, P; Blum, L; Burns, D; Connes, A; Donnelly, H; Ebin, D; Guillemin, V; Palais, R; Rossi, H; Simons, J; Singer, E; Singer, N; Stanton, N; Sternberg, S, Isadore M. Singer (1924–2021) In Memoriam Part 2: Personal Recollections, Notices of the American Mathematical Society, vol. 69 no. 10 (November, 2022), pp. 1-1, American Mathematical Society (AMS)
  4. Bryant, R; Bismut, J-M; Cheeger, J; Griffiths, P; Donaldson, S; Hitchin, N; Lawson, HB; Gromov, M; Marcus, A; Spielman, D; Srivastava, N; Witten, E, Isadore M. Singer (1924–2021) In Memoriam Part 1: Scientific Works, Notices of the American Mathematical Society, vol. 69 no. 09 (October, 2022), pp. 1-1, American Mathematical Society (AMS)
  5. Phong, DH; Siu, Y-T; Bryant, R; Chau, A; Falbel, E; Fefferman, C; Friedman, R; Morgan, J; Futaki, A; Griffiths, P; Kohn, JJ; Mok, N; Mori, S; Namba, M; Noguchi, J; Ohsawa, T; Sato, M; Yau, S-T, Masatake Kuranishi (1924–2021), Notices of the American Mathematical Society, vol. 69 no. 05 (May, 2022), pp. 1-1, American Mathematical Society (AMS)
  6. Bryant, RL, S.-S. Chern’s study of almost-complex structures on the six-sphere, edited by Bryant, R; Cheng, SY; Griffiths, P; Ma, X; Ni, L; Wallach, N, International Journal of Mathematics, vol. 32 no. 12 (November, 2021), World Scientific Publishing
  7. Bryant, RL; Foulon, P; Ivanov, SV; Matveev, VS; Ziller, W, Geodesic behavior for Finsler metrics of constant positive flag curvature on S2, Journal of Differential Geometry, vol. 117 no. 1 (January, 2021), pp. 1-22
  8. Acharya, BS; Bryant, RL; Salamon, S, A circle quotient of a G2 cone, Differential Geometry and its Application, vol. 73 (December, 2020), pp. 43 pages, Elsevier
  9. Bryant, RL, Notes on spinors in low dimension (November, 2020)
  10. Bryant, RL; Clelland, JN, Flat metrics with a prescribed derived coframing, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), vol. 16 (January, 2020), National Academy of Science of Ukraine
  11. Bryant, RL; Eastwood, MG; Gover, AR; Neusser, K, Some differential complexes within and beyond parabolic geometry, Advanced Studies in Pure Mathematics, vol. 82 no. Differential Geometry and Tanaka Theory (November, 2019), pp. 13-40, Mathematical Society of Japan
  12. 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
  13. Bryant, RL, Notes on Projective, Contact, and Null Curves (May, 2019)
  14. 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
  15. Bryant, RL, On the Convex Pfaff-Darboux Theorem of Ekeland and Nirenberg, SIGMA 19, vol. 060 (December, 2015), pp. 10
  16. Bryant, RL, On the conformal volume of 2-tori (July, 2015)
  17. Bryant, RL, Notes on exterior differential systems (May, 2014)
  18. Bryant, RL, Complex analysis and a class of Weingarten surfaces (May, 2011), pp. 10 pages
  19. Bryant, R; Xu, F, Laplacian Flow for Closed $G_2$-Structures: Short Time Behavior (January, 2011)
  20. Bryant, RL, Non‐Embedding and Non‐Extension 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 0199534926
  21. 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
  22. with Bryant, R; Dunajski, M; Eastwood, M, Metrisability of two-dimensional projective structures, Journal of Differential Geometry, vol. 83 no. 3 (January, 2009), pp. 465-500, International Press of Boston, ISSN 0022-040X
  23. Bryant, RL, GRADIENT KAHLER RICCI SOLITONS, in Géométrie différentielle, physique mathématique, mathématiques et société. I., Astérisque, ASTERISQUE, vol. 321 no. 321 (Spring, 2008), pp. 51-97, SOC MATHEMATIQUE FRANCE, ISBN 978-285629-258-7
  24. 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
  25. Bryant, RL, GEODESICALLY REVERSIBLE FINSLER 2-SPHERES OF CONSTANT CURVATURE, in Nankai Tracts in Mathematics, Nankai Tracts in Mathematics, edited by Griffiths, PA, vol. 11 (Winter, 2006), pp. 95-111, WORLD SCIENTIFIC, ISBN 9789812700612
  26. Bryant, RL, On the geometry of almost complex 6-manifolds, ASIAN JOURNAL OF MATHEMATICS, vol. 10 no. 3 (September, 2006), pp. 561-605, INT PRESS
  27. Bryant, RL, CONFORMAL GEOMETRY AND 3-PLANE FIELDS ON 6-MANIFOLDS(Developments of Cartan Geometry and Related Mathematical Problems), in Developments of Cartan Geometry and Related Mathematical Problems, RIMS Symposium Proceedings, 数理解析研究所講究録, vol. 1502 (July, 2006), pp. 1-15, 京都大学
  28. Bryant, RL, SO(n)-Invariant special lagrangian submanifolds of Cn+1 with fixed loci, CHINESE ANNALS OF MATHEMATICS SERIES B, vol. 27 no. 1 (January, 2006), pp. 95-112, SHANGHAI SCIENTIFIC TECHNOLOGY LITERATURE PUBLISHING HOUSE
  29. Bryant, R; Freed, D, Shiing-Shen Chern, Physics Today, vol. 59 no. 1 (January, 2006), pp. 70-72, AIP Publishing
  30. 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
  31. 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, 150 Years of Mathematics at Washington University in St. Louis, vol. 395 (January, 2006), pp. 29-38, AMER MATHEMATICAL SOC, ISBN 0-8218-3603-X
  32. 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.)
  33. Bryant, RL, Real hypersurfaces in unimodular complex surfaces (July, 2004)
  34. with Bryant, R; Edelsbrunner, H; Koehl, P; Levitt, M, The area derivative of a space-filling diagram, Discrete and Computational Geometry, vol. 32 no. 3 (January, 2004), pp. 293-308, Springer Nature (ISSN: 0179-5376.)
  35. Bryant, RL, Some remarks on G_2-structures, in Proceedings of Gökova Geometry-Topology Conference 2005, edited by Akbulut, S; Onder, T; Stern, R (May, 2003), pp. 75-109, International Press, ISBN 1-57146-152-3
  36. 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
  37. 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
  38. Bryant, RI, On Surfaces with Prescribed Shape Operator, Results in Mathematics, vol. 40 no. 1-4 (October, 2001), pp. 88-121, Springer Science and Business Media LLC (Dedicated to Shiing-Shen Chern on his 90th birthday.)
  39. Bryant, RL, Bochner-Kahler metrics, JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 14 no. 3 (January, 2001), pp. 623-715, AMER MATHEMATICAL SOC
  40. Bryant, RL, Calibrated embeddings in the special Lagrangian and coassociative cases, ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, vol. 18 no. 3-4 (August, 2000), pp. 405-435, SPRINGER (Special issue in memory of Alfred Gray (1939--1998).)
  41. Bryant, RL, Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces (June, 2000)
  42. 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 (April, 2000), pp. 53-94, Société Mathématique de France, ISBN 2-85629-094-9
  43. Bryant, RL, Harmonic morphisms with fibers of dimension one, COMMUNICATIONS IN ANALYSIS AND GEOMETRY, vol. 8 no. 2 (April, 2000), pp. 219-265, INT PRESS CO LTD
  44. Bryant, R, Recent advances in the theory of holonomy, ASTERISQUE, vol. 266 no. 266 (January, 2000), pp. 351-+, SOC MATHEMATIQUE FRANCE (Exposé No. 861.)
  45. 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
  46. Bryant, RL, Recent Advances in the Theory of Holonomy, Seminaire Bourbaki, vol. 1998 no. 99 (October, 1999), pp. 351-374
  47. Bryant, RL, Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms, Adv. Stud. Pure Math., 37, Math. Soc. Japan, Tokyo, 2002, 1--44 (September, 1999)
  48. Bryant, RL, Some examples of special Lagrangian tori, Advances in Theoretical and Mathematical Physics, vol. 3 no. 1 (1999), pp. 83-90, International Press of Boston
  49. 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, Elsevier BV
  50. 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
  51. Bryant, RL, Projectively flat Finsler 2-spheres of constant curvature, Selecta Mathematica, vol. 3 no. 2 (March, 1997), pp. 161-203, Springer Science and Business Media LLC
  52. 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
  53. 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
  54. with Bryant, R; Griffiths, P; Hsu, L, Hyperbolic exterior differential systems and their conservation laws, part II, Selecta Mathematica, New Series, vol. 1 no. 2 (September, 1995), pp. 265-323, Springer Nature
  55. Bryant, RL; Griffiths, PA, Characteristic Cohomology of Differential Systems (I): General Theory, Journal of the American Mathematical Society, vol. 8 no. 3 (July, 1995), pp. 507-507, JSTOR
  56. BRYANT, RL; GRIFFITHS, PA, CHARACTERISTIC COHOMOLOGY OF DIFFERENTIAL-SYSTEMS .1. GENERAL-THEORY, JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 8 no. 3 (July, 1995), pp. 507-596, AMER MATHEMATICAL SOC
  57. with BRYANT, RL; GRIFFITHS, PA, CHARACTERISTIC COHOMOLOGY OF DIFFERENTIAL-SYSTEMS .2. CONSERVATION-LAWS FOR A CLASS OF PARABOLIC EQUATIONS, DUKE MATHEMATICAL JOURNAL, vol. 78 no. 3 (June, 1995), pp. 531-676, DUKE UNIV PRESS
  58. with Bryant, R; Griffiths, P; Hsu, L, Hyperbolic exterior differential systems and their conservation laws, part I, Selecta Mathematica, New Series, vol. 1 no. 1 (March, 1995), pp. 21-112, Springer Nature
  59. 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
  60. 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
  61. 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
  62. 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 (June, 1994), pp. 86-111, Cambridge University Press, ISBN 0-521-56216-3
  63. 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
  64. Bryant, RL, Some remarks on the geometry of austere manifolds, Boletim da Sociedade Brasileira de Matemática, vol. 21 no. 2 (September, 1991), pp. 133-157, Springer Nature
  65. 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
  66. 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)
  67. 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
  68. 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
  69. 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
  70. Bryant, RL, Metrics with Exceptional Holonomy, The Annals of Mathematics, vol. 126 no. 3 (November, 1987), pp. 525-525, JSTOR
  71. 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
  72. 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
  73. 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
  74. with BRYANT, R; GRIFFITHS, P, REDUCTION FOR CONSTRAINED VARIATIONAL-PROBLEMS AND INTEGRAL-K2/2DS, AMERICAN JOURNAL OF MATHEMATICS, vol. 108 no. 3 (June, 1986), pp. 525-570, JOHNS HOPKINS UNIV PRESS
  75. Bryant, RL, Minimal surfaces of constant curvature in sn, Transactions of the American Mathematical Society, vol. 290 no. 1 (January, 1985), pp. 259-271, JSTOR
  76. Bryant, RL, Lie groups and twlstor spaces, Duke Mathematical Journal, vol. 52 no. 1 (January, 1985), pp. 223-261, Duke University Press
  77. 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
  78. 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
  79. 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
  80. 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
  81. 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
  82. 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)
  83. 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
  84. 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
  85. 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
  86. with BERGER, E; BRYANT, R; GRIFFITHS, P, SOME ISOMETRIC EMBEDDING AND RIGIDITY RESULTS FOR RIEMANNIAN-MANIFOLDS, PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA-PHYSICAL SCIENCES, 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)

Preprints

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