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Publications of Robert Bryant    :chronological  alphabetical  combined  bibtex listing:



  1. with David Bao, S.-S. Chern, 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(2005j:53003)]
  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]  [author's comments]
  3. 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]
  4. Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces, Annals of Mathematics Studies (to appear) [math.DG/0006186]  [author's comments]
  5. with S.-S. Chern, Robert B. Gardner, Hubert L. Goldschmidt,and Phillip A. Griffiths, Exterior Differential Systems, MSRI Publications18. Springer-Verlag, New York, 1991 [MR92h:58007]  [author's comments]
  6. with Victor Guillemin, Sigurdur Helgason, and R. O. Wells, Jr. (eds.), Integral Geometry, Proceedings of the AMS-IMS-SIAM joint summer research conference held in Brunswick, Maine, August 12--18, 1984, pp. x+350, 1987, American Mathematical Society, [MR87j:53003]
  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 [MR88b:53002]

Papers Published

  1. RL Bryant, Non-Embedding and Non-Extension Results in Special Holonomy, in The many facets of geometry, edited by Jean-Pierre Bourguignon, Simon Salamon, and Oscar Garcia Prada, The Many Facets of Geometry: A Tribute to Nigel Hitchin (Fall, 2010), pp. 346--367, Oxford University Press, Oxford [MR2681703], [doi]  [abs]
  2. RL Bryant, Commentary, Bulletin of the American Mathematical Society, vol. 46 no. 2 (2009), pp. 177-178, ISSN 0273-0979 [doi]
  3. with M Dunajski and M Eastwood, Metrisability of two-dimensional projective structures, J. 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 G Manno and V 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 [3592]  [abs]
  6. RL Bryant, Gradient Kahler Ricci solitons, Asterisque no. 321 (2008), pp. 51-97, ISSN 0303-1179  [abs]
  7. 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 [math.DG/0407514]  [abs]
  8. RL Bryant, 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]
  9. 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]  [abs] [author's comments]
  10. RL Bryant, 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]
  11. 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 [math.DG/0007128]  [abs]
  12. Some remarks on G2 structures, in Proceeding of Gökova Geometry-Topology Conference 2005, edited by S. Akbulut, T Önder, and R.J. Stern (2006), International Press [math.DG/0305124]  [abs]
  13. 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]  [author's comments]
  14. Holonomy and Special Geometries, in Dirac Operators: Yesterday and Today, Conference Proceedings and Lecture Notes in Geometry and Topology, edited by Bourguignon, Branson, Chamseddine, Hijazi, and Stanton (2005), pp. 71--90, International Press (Proceedings of the Summer School and Workshop at CAMS-AUB, Lebanon, August 27 -- September 7, 2001.) [MR2205367]
  15. with R Bryant, H Edelsbrunner, P Koehl and M Levitt, 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]
  16. 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]
  17. RL Bryant, 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]
  18. RL Bryant, 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]
  19. RL Bryant, Bochner-Kähler metrics, Journal of the AMS, vol. 14 no. 3 (2001), pp. 623-715 [MR2002i:53096], [math.DG/0003099]  [abs]
  20. Élie Cartan and geometric duality, in Journées Élie Cartan 1998 et 1999, vol. 16 (2000), pp. 5–20, Institut Élie Cartan [pdf]  [author's comments]
  21. Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor, in Global Analysis and Harmonic Analysis, Séminaires & Congrès, vol. 4 (2000), pp. 53–93 [MR2002h:53082], [math.DG/0004073]  [abs]
  22. RL Bryant, Recent advances in the theory of holonomy, Astérisque, vol. 266 no. 5 (2000), pp. 351-374 (Exposé No. 861.) [MR2001h:53067], [math.DG/9910059], [html]  [author's comments]
  23. RL Bryant, 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]
  24. RL Bryant, 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]
  25. RL Bryant, 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]
  26. RL Bryant, Some examples of special Lagrangian tori, Adv. Theor. Math. Phys., vol. 3 no. 1 (1999), pp. 83–90 [MR2000f:32033], [math.DG/9902076]  [abs]
  27. with Eric Sharpe, D-branes and Spinc-structures, Phys. Lett. B, vol. 450 no. 4 (1999), pp. 353–357 [MR2000c:53054], [hep-th/98l2084]  [abs]
  28. RL Bryant and E Sharpe, D-branes and Spinc structures, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, vol. 450 no. 4 (1999), pp. 353-357  [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. RL Bryant, 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. On extremals with prescribed Lagrangian densities, in Manifolds and geometry (Pisa, 1993), Symposia Mathematica, edited by Paolo de Bartolomeis, Franco Tricerri and Edoardo Vesentini, vol. XXXVI (1996), pp. 86–111, Cambridge Univ. Press, Cambridge [MR99a:58043], [dg-ga/9406001]  [author's comments]
  32. Classical, exceptional, and exotic holonomies: a status report, in Actes de la Table Ronde de Géométrie Différentielle (Luminy, 1992), Sémin. Congr., vol. 1 (1996), pp. 93–165, Soc. Math. France, Paris [MR98c:53037], [dvi]  [abs]
  33. 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]
  34. with Phillip Griffiths and Lucas Hsu, Toward a geometry of differential equations, in Geometry, Topology, & Physics, Conf. Proc. Lecture Notes Geom. Topology, edited by S.-T. Yau, vol. IV (1995), pp. 1–76, Internat. Press, Cambridge, MA [MR97b:58005], [dvi]
  35. with Robert B. Gardner, Control structures, in Geometry in nonlinear control and differential inclusions (Warsaw, 1993), Banach Center Publications, edited by Bronis\l aw Jakubczyk, Witold Respondek and Tadeusz Rze\.zuchowski, vol. 12 (1995), pp. 111–121, Polish Acad. Sci., Warsaw [MR96h:93024], [dvi]
  36. An introduction to Lie groups and symplectic geometry, in Geometry and quantum field theory (Park City, UT, 1991), IAS/Park City Mathematics, vol. 1 (1995), pp. 5–181, Amer. Math. Soc., Providence, RI [MR96i:58002]  [abs] [author's comments]
  37. with PA Griffiths and L Hsu, 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]
  38. with PA Griffiths and L Hsu, 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]
  39. with Phillip Griffiths, 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]
  40. with Phillip Griffiths, 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]
  41. with Lucas Hsu, Rigidity of integral curves of rank 2 distributions, Invent. Math., vol. 114 no. 2 (1993), pp. 435–461, ISSN 0020-9910 [MR94j:58003], [dvi], [doi]  [author's comments]
  42. RL Bryant and L Hsu, Rigidity of integral curves of rank 2 distributions, Inventiones Mathematicae, vol. 114 no. 1 (1993), pp. 435-461, ISSN 0020-9910 [doi]
  43. 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 James A. Carlson, C. Herbert Clemens and David R. Morrison, vol. 53 (1991), pp. 33–88, Amer. Math. Soc., Providence, RI [MR93e:53030], [dvi]  [author's comments]
  44. RL Bryant, 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]
  45. with F Reese Harvey, Submanifolds in hyper-Kähler geometry, J. Amer. Math. Soc., vol. 2 no. 1 (1989), pp. 1–31 [MR89m:53090]  [author's comments]
  46. with Simon Salamon, 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]
  47. Surfaces in conformal geometry, in The mathematical heritage of Hermann Weyl (Durham, NC, 1987), Proc. Sympos. Pure Math., vol. 48 (1988), pp. 227–240, Amer. Math. Soc., Providence, RI [MR89m:53102]  [author's comments]
  48. Surfaces of mean curvature one in hyperbolic space, in Théorie des variétés minimales et applications (Palaiseau, 1983–1984), Astérisque, vol. 154-155 (1987) (1988), pp. 321–347, Société Mathématique de France, Paris [MR955072]  [author's comments]
  49. 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 Mladen Luksic, Clyde Martin and William Shadwick, vol. 68 (1987), pp. 65–76, Amer. Math. Soc., Providence, RI [MR89f:58037]  [author's comments]
  50. A survey of Riemannian metrics with special holonomy groups, in Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), (1987), pp. 505–514, Amer. Math. Soc., Providence, RI [MR89f:53068]  [author's comments]
  51. Minimal Lagrangian submanifolds of Kähler-Einstein manifolds, in Differential geometry and differential equations (Shanghai, 1985), Lecture Notes in Math., edited by Chao Hao Gu, Marcel Berger and Robert L. Bryant, vol. 1255 (1987), pp. 1–12, Springer-Verlag, Berlin [MR88j:53061]  [author's comments]
  52. RL Bryant, Metrics with exceptional holonomy, Ann. of Math. (2), vol. 126 no. 3 (1987), pp. 525–576 [MR89b:53084]  [author's comments]
  53. with Phillip Griffiths, 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]
  54. Metrics with holonomy G2 or Spin(7), in Workshop Bonn 1984 (Bonn, 1984), Lecture Notes in Math., edited by F. Hirzebruch, J. Schwermer and S. Suter, vol. 1111 (1985), pp. 269–277, Springer, Berlin--New York [MR87a:53082]  [author's comments]
  55. RL Bryant, Minimal surfaces of constant curvature in Sn, Trans. Amer. Math. Soc., vol. 290 no. 1 (1985), pp. 259–271 [MR87c:53110]  [author's comments]
  56. RL Bryant, Lie groups and twistor spaces, Duke Math. J., vol. 52 no. 1 (1985), pp. 223–261 [MR87d:58047]  [author's comments]
  57. RL Bryant, A duality theorem for Willmore surfaces, J. Differential Geom., vol. 20 no. 1 (1984), pp. 23–53 [MR86j:58029]  [author's comments]
  58. with Phillip A. Griffiths, 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 Michael Artin and John Tate, vol. 36 (1983), pp. 77–102, Birkhäuser Boston, Boston, MA [MR86a:32044]  [author's comments]
  59. with P Griffiths and D Yang, Characteristics and existence of isometric embeddings, Duke Math. J., vol. 50 no. 4 (1983), pp. 893–994 [MR85d:53027]  [author's comments]
  60. with E Berger and P Griffiths, The Gauss equations and rigidity of isometric embeddings, Duke Math. J., vol. 50 no. 3 (1983), pp. 803–892 [MR85k:53056]  [author's comments]
  61. with Shiing-Shen Chern and Phillip Griffiths, Exterior differential systems, in Proceedings of the 1980 Beijing Symposium on Differential Geometry and Differential Equations (Beijing, 1980), edited by S. S. Chern and Wen Tsün Wu, vol. 1 (1982), pp. 219–338, Science Press, Beijing [MR85k:58005]  [author's comments]
  62. RL Bryant, Holomorphic curves in Lorentzian CR-manifolds, Trans. Amer. Math. Soc., vol. 272 no. 1 (1982), pp. 203–221 [MR83i:32029]  [abs]
  63. RL Bryant, Submanifolds and special structures on the octonians, J. Differential Geom., vol. 17 no. 2 (1982), pp. 185–232 [MR84h:53091]  [abs]
  64. RL Bryant, 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]
  65. with E Berger and P Griffiths, 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]


  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]
ph: 919.660.2800
fax: 919.660.2821

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