Publications of Robert L. Bryant

Each entry is followed by either a Math Review link (which requires a subscription to Math Reviews), a link to a source, or both.


  1. with David Bao, S.-S. Chern and Zhongmin Shen, eds., A sampler of Riemann-Finsler geometry, Mathematical Sciences Research Institute Publications, edited by Bao, David and Bryant, Robert L. and Chern, Shiing-Shen, vol. 50 (2004), pp. xii+363, Cambridge University Press, Cambridge. [MR2132655]
  2. with Phillip Griffiths and Dan Grossmann, Exterior Differential Systems and Euler-Lagrange Partial Differential Equations, Chicago Lectures in Mathematics (2003), University of Chicago Press (vii+213 pages, ISBN: 0-226-07794-2.) [MR1985469] [math.DG/0207039]
  3. with David R. Morrison (eds.), Selected works of Phillip A. Griffiths with commentary. Part 4: Differential systems, (2003), American Mathematical Society, Providence, RI; International Press, Somerville, MA. [MR2005e:01025d]
  4. Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces, Annals of Mathematics Studies (to appear). [math.DG/0006186]
  5. with S.-S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, and Phillip A. Griffiths, Exterior differential systems, MSRI Publications 18. Springer-Verlag, New York, 1991. [MR 92h:58007]
  6. with Chao Hao Gu and Marcel Berger (eds.), Differential geometry and differential equations, Proceedings of the sixth symposium held at Fudan University, Shanghai, June 21 – July 6, 1985. [MR 88b:53002]
  7. with Victor Guillemin, Sigurdur Helgason, and R. O. Wells, Jr. (eds.), Integral geometry, Contemporary Mathematics 63. AMS, Providence, R.I., 1987. [MR 87j:53003]

Preprints and unpublished manuscripts

  1. with Michael G. Eastwood, A. Rod. Gover, and Katharina Neusser, Some differential complexes within and beyond parabolic geometry (2011) [arXiv:1112.2142]
  2. with Feng Xu, Laplacian Flow for Closed G2-Structures: Short Time Behavior (2011) [arXiv:1101.2004]
  3. Real hypersurfaces in unimodular complex surfaces (2004) [math.DG/0407472]
  4. Complex analysis and a class of Weingarten surfaces (1984) [arXiv:1105.5589]

Published Papers

  1. Non-embedding and non-extension results in special holonomy, in The many facets of geometry, 346–367, Oxford University Press, Oxford, 2010. [MR2681703]
  2. with Maciej Dunajski and Michael Eastwood, Metrisability of two-dimensional projective structures, J. Differential Geometry, vol. 83 no. 3 (2009), pp. 465–499. [MR2581355] [arXiv:0801.0300]
  3. Gradient Kähler Ricci Solitons, in Géométrie différentielle, physique mathématique, mathématiques et société. I., Astérisque, vol. 321 (Spring, 2008), pp. 51–97. [MR2010i:53138] [math.DG/0407453]
  4. with Gianni Manno and Vladimir Matveev, 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. [MR2368987] [math.DG/07053592]
  5. 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 P. A. Griffiths, vol. 11 (Winter, 2006), World Scientific. [MR2313331] [math.DG/0407514]
  6. On the geometry of almost complex 6-manifolds, The Asian Journal of Mathematics, vol. 10 no. 3 (September, 2006), pp. 561–606. [MR2253159] [math.DG/0508428]
  7. Conformal geometry and 3-plane fields on 6-manifolds, in Developments of Cartan Geometry and Related Mathematical Problems, RIMS Symposium Proceedings, vol. 1502 (July, 2006), pp. 1–15, Kyoto University. [math.DG/0511110]
  8. SO(n)-invariant special Lagrangian submanifolds of $\mathbb{C}^{n+1}$ with fixed loci, Chinese Annals of Mathematics, Series B, vol. 27 no. 1 (January, 2006), pp. 95–112. [MR2209954] [math.DG/0402201]
  9. 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, vol. 40 (2006), American Mathematical Society. [MR2237106] [math.DG/0007128]
  10. Some remarks on $G_2$ structures, in Proceeding of Gokova Geometry-Topology Conference 2005, 75–109, Gokova Geometry/Topology Conference (GGT), Gokova, 2006. [MR2282011] [math.DG/0305124]
  11. Geometry of manifolds with special holonomy: "100 years of holonomy", in 150 years of mathematics at Washington University in St. Louis, Contemporary Mathematics, vol. 395 (2006), pp. 29–38, AMS. [MR2206889] [MR2206889]
  12. Holonomy and Special Geometries, in Dirac Operators: Yesterday and Today, 71–90, International Press, Sommerville, MA, 2005. [MR2205367]
  13. with Herbert Edelsbrunner, Patrice Koehl, and Michael Levitt, The area derivative of a space-filling diagram, Discrete & Computational Geometry. An International Journal of Mathematics and Computer Science, vol. 32 no. 3 (2004), pp. 293–308. [MR2005k:92077]
  14. Some remarks on Finsler manifolds with constant flag curvature, Special issue for S.-S. Chern, Houston Journal of Mathematics, 28 (2002), no. 2, 221–262. [MR2003h:53102] [math.DG/0107228]
  15. On surfaces with prescribed shape operator, Dedicated to Shiing-Shen Chern on his 90th birthday, Results Math. 40 (2001), no. 1–4, 88–121. [MR2002i:53010] [math.DG/0107083]
  16. Bochner-Kähler metrics, Journal of the AMS, 14 (2001), 623–715. [MR1824987] [math.DG/0003099]
  17. Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor, in Global Analysis and Harmonic Analysis, Séminaires & Congrès 4 (2000), 53–93. [MR1822355] [math.DG/0004073]
  18. Levi-flat minimal hypersurfaces in two-dimensional complex space forms, Lie Groups, Geometric Structures and Differential Equations, Advanced Studies in Pure Mathematics, 2000. [MR1980895] [math.DG/9909159]
  19. Calibrated embeddings in the special Lagrangian and coassociative cases, Annals of Global Analysis and Geometry 18 (2000), pp. 405-435. [MR1795105] [math.DG/9912246]
  20. Élie Cartan and geometric duality, Journées Élie Cartan 1998 et 1999, Institut Élie Cartan 16 (2000), 5–20. [Cartan.pdf]
  21. Recent Advances in the Theory of Holonomy, (Exposé 861), Séminaire Bourbaki, Volume 1998/99, Astérisque 266 (2000), 351–374. [MR1772679] [math.DG/9910059]
  22. Some Examples of Special Lagrangian Tori, Adv. Theor. Math. Phys. 1 (1999), 83–90. [MR2000f:32033] [math.DG/9902076]
  23. with Eric R. Sharpe, $D$-Branes and Spinc Structures, Physics Letters B 450 (1999), 353–357. [MR2000c:53054] [hep-th/9812084]
  24. Projectively Flat Finsler 2-Spheres of Constant Curvature, Selecta Mathematica, (N. S.) 3 (1997), 161–203. [MR98i:53101] [dg-ga/9611010]
  25. Harmonic morphisms with fibers of dimension one, Communications in Analysis and Geometry 8 (2000), 219–265 [MR1753318] [dg-ga/9701002]
  26. Classical, Exceptional, and Exotic Holonomies: A Status Report, Actes de la Table Ronde de Geometrie Differentielle en l'Honneur de Marcel Berger, Collection SMF, Séminaires & Congres, 1 (1996), 93-166. [MR 98c:53037] [95-10.dvi]
  27. On Extremals with Prescribed Lagrangian Densities, Manifolds and Geometry, Symposia Mathematica XXXVI (1996), Cambridge University Press, 86–111. [MR 99a:58043] [dg-ga/9406001]
  28. Finsler Structures on the 2-Sphere Satisfying $K=1$, Finsler Geometry, Contemporary Mathematics 196 (1996), AMS Publications, 27–42. [MR 97e:53128] [95-11.dvi]
  29. with Phillip A. Griffiths, Characteristic Cohomology of Differential Systems, I: General Theory, Journal of the AMS 8 (1995), 507–596. [MR 96c:58183] [93-01.dvi]
  30. with Phillip A. Griffiths, Characteristic Cohomology of Differential Systems, II: Conservation Laws for a Class of Parabolic Equations, Duke Mathematical Journal 78 (1995), 531–676. [MR 96d:58158] [93-02.dvi]
  31. with Lucas Hsu and Phillip A. Griffiths, Hyperbolic Exterior Differential Systems and Their Conservation Laws, Part I, Selecta Math. (N.S.) 1 (1995), 21–112. [MR 97d:580008] [94-13.dvi]
  32. with Lucas Hsu and Phillip A. Griffiths, Hyperbolic Exterior Differential Systems and Their Conservation Laws, Part II, Selecta Math. (N.S.) 1 (1995), 265–323. [MR 97d:580009] [94-13.dvi]
  33. with Lucas Hsu and Phillip A. Griffiths, Toward a Geometry of Differential Equations, Geometry, Topology & Physics, 1–76, Conf. Proc. Lecture Notes Geom. Topology, VI, Internat. Press, Cambridge, MA, 1995. [MR 97b:58005] [94-12.dvi]
  34. with Robert B. Gardner, Control Structures, in Geometry in Nonlinear Control and Differential Inclusions, Banach Center Publications 32 (1995), Institute of Mathematics, Polskeij Akademii Nauk, Warszawa, Poland. [MR 96h:93024] [94-11.dvi]
  35. An introduction to Lie groups and symplectic geometry, in Geometry and quantum field theory (Park City, UT, 1991), 5–181, IAS/Park City Math. Ser. 1, Amer. Math. Soc., Providence, RI, 1995. [MR 96i:58002]
  36. with Lucas Hsu, Rigidity of integral curves of rank 2 distributions, Invent. Math. 114 (1993), 435–461. [MR 94j:58003] [Rigid.dvi]
  37. Two exotic holonomies in dimension four, path geometries, and twistor theory, Complex geometry and Lie theory (Sundance, UT, 1989), 33–88, Proc. Sympos. Pure Math. 53, Amer. Math. Soc., Providence, RI, 1991. [MR 93e:53030] [ExoticHol.dvi]
  38. Some remarks on the geometry of austere manifolds, Bol. Soc. Brasil. Mat. (N.S.) 21 (1991), 133–157. [MR 92k:53112] [90-03.dvi]
  39. with Simon M. Salamon, On the construction of some complete metrics with exceptional holonomy, Duke Math. J. 58 (1989), 829–850. [MR 90i:53055]
  40. Surfaces in conformal geometry, in The mathematical heritage of Hermann Weyl (Durham, NC, 1987), 227–240, Proc. Sympos. Pure Math. 48, Amer. Math. Soc., Providence, RI, 1988. [MR 89m:53102]
  41. with Reese Harvey, Submanifolds in hyper-Kähler geometry, J. Amer. Math. Soc. 2 (1989), 1–31. [MR 89m:53090]
  42. Metrics with exceptional holonomy, Ann. of Math. (2) 126 (1987), 525–576. [MR 89b:53084]
  43. A survey of Riemannian metrics with special holonomy groups, Proceedings of the International Congress of Mathematicians, Vol. 1 (Berkeley, CA, 1986), 505–514, Amer. Math. Soc., Providence, RI, 1987. [MR 89f:53068]
  44. On notions of equivalence of variational problems with one independent variable, in Differential geometry: the interface between pure and applied mathematics (San Antonio, TX, 1986), 65–76, Contemp. Math. 68, AMS, Providence, RI, 1987. [MR 89f:58037]
  45. Lie groups and twistor spaces, Duke Math. J. 52 (1985), 223–261. [MR 87d:58047]
  46. Metrics with holonomy $G_2$ or Spin(7), Workshop Bonn 1984 (Bonn, 1984), 269–277, Lecture Notes in Math. 1111, Springer, Berlin–New York, 1985. [MR 87a:53082]
  47. Minimal Lagrangian submanifolds of Kähler-Einstein manifolds, Differential geometry and differential equations (Shanghai, 1985), 1–12, Lecture Notes in Math. 1255, Springer, Berlin-New York, 1987. [MR 87a:53082]
  48. Surfaces of mean curvature one in hyperbolic space, Théorie des variétés minimales et applications (Palaiseau, 1983–1984). Astérisque 154–155 (1987), 321–347. CMP: 955 072.
  49. with Phillip. A. Griffiths, Reduction for constrained variational problems and $\int{1\over 2}\kappa^2\,ds$, Amer. J. Math. 108 (1986), 525–570. [MR 88a:58044]
  50. Minimal surfaces of constant curvature in $S^n$, Trans. Amer. Math. Soc. 290 (1985), 259–271. [MR 87c:53110]
  51. A duality theorem for Willmore surfaces, J. Differential Geom. 20 (1984), 23–53. [MR 86j:58029]
  52. with Phillip A. Griffiths, Some observations on the infinitesimal period relations for regular threefolds with trivial canonical bundle, Arithmetic and geometry, Vol. II, 77–102, Progr. Math. 36, Birkhauser, Boston, Mass., 1983. [MR 86a:32044]
  53. with Eric Berger and Phillip A. Griffiths, The Gauss equations and rigidity of isometric embeddings, Duke Math. J. 50 (1983), 803–892. [MR 85k:53056]
  54. with Phillip A. Griffiths and Deane Yang, Characteristics and existence of isometric embeddings, Duke Math. J. 50 (1983), 893–994. [MR 85k:53056]
  55. with Shiing-Shen Chern and Phillip A. Griffiths, Exterior differential systems, Proceedings of the 1980 Beijing Symposium on Differential Geometry and Differential Equations, Vol. 1 (Beijing, 1980), 219–338, Science Press, Beijing, 1982. [MR 85k:58005]
  56. Submanifolds and special structures on the octonians, J. Differential Geom. 17 (1982), 185–232. [MR 84h:53091]
  57. Conformal and minimal immersions of compact surfaces into the 4-sphere, J. Differential Geom. 17 (1982), 455–473. [MR 84a:53062]
  58. with Eric Berger and Phillip A. Griffiths, Some isometric embedding and rigidity results for Riemannian manifolds, Proc. Nat. Acad. Sci. U.S.A. 78 (1981), no. 8, part 1, 4657–4660. [MR 82h:53074]
  59. Holomorphic curves in Lorentzian CR-manifolds, Trans. Amer. Math. Soc. 272 (1982), 203–221. [MR 83i:32029]