Now showing items 1-13 of 13

    • An introduction to Lie groups and symplectic geometry 

      Bryant, R (Geometry and quantum field theory (Park City, UT, 1991)IAS/Park City Mathematics Series, 1995)
    • Complex analysis and a class of Weingarten surfaces 

      Bryant, R (2011-05-27)
      An idea of Hopf's for applying complex analysis to the study of constant mean curvature spheres is generalized to cover a wider class of spheres, namely, those satisfying a Weingarten relation of a certain type, namely H ...
    • Élie Cartan and geometric duality 

      Bryant, R (Journées Élie Cartan 1998 et 1999, 2000)
    • Geodesic behavior for Finsler metrics of constant positive flag curvature on S^2 

      Bryant, R; Foulon, P; Ivanov, S; Matveev, VS; Ziller, W
      We study non-reversible Finsler metrics with constant flag curvature 1 on S^2 and show that the geodesic flow of every such metric is conjugate to that of one of Katok's examples, which form a 1-parameter family. In particular, ...
    • Geodesically reversible Finsler 2-spheres of constant curvature 

      Bryant, R (Inspired by S. S. Chern---A Memorial Volume in Honor of a Great MathematicianNankai Tracts in Mathematics, 2006)
      A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need ...
    • Holonomy and Special Geometries 

      Bryant, R (Dirac Operators: Yesterday and TodayConference Proceedings and Lecture Notes in Geometry and Topology, 2005)
    • Laplacian Flow for Closed $G_2$-Structures: Short Time Behavior 

      Bryant, R; Xu, F (2011-01-11)
      We prove short time existence and uniqueness of solutions to the Laplacian flow for closed $G_2$ structures on a compact manifold $M^7$. The result was claimed in \cite{BryantG2}, but its proof has never appeared.
    • Metrisability of two-dimensional projective structures 

      Bryant, R; Dunajski, M; Eastwood, M (Journal of Differential Geometry, 2009-12-01)
      We carry out the programme of R. Liouville [19] to construct an explicit local obstruction to the existence of a Levi-Civita connection within a given projective structure [Γ] on a surface. The obstruction is of order 5 ...
    • On extremals with prescribed Lagrangian densities 

      Bryant, R (Manifolds and geometry (Pisa, 1993)Symposia Mathematica, 1996)
      This article studies some examples of the family of problems where a Lagrangian is given for maps from one manifold to another and one is interested in the extremal mappings for which the Lagrangian density takes a prescribed ...
    • Pseudo-Reimannian metrics with parallel spinor fields and vanishing Ricci tensor 

      Bryant, R (Global analysis and harmonic analysis (Marseille-Luminy, 1999)Séminaires et Congrès, 2000)
      I discuss geometry and normal forms for pseudo-Riemannian metrics with parallel spinor fields in some interesting dimensions. I also discuss the interaction of these conditions for parallel spinor fields with the condition ...
    • Recent advances in the theory of holonomy 

      Bryant, R (Asterisque, 2000-12-01)
      After its introduction by Élie Cartan, the notion of holonomy has become increasingly important in Riemannian and affine geometry. Beginning with the fundamental work of Marcel Berger, the classification of possible holonomy ...
    • Some remarks on G2-structures 

      Bryant, R (Proceedings of Gökova Geometry-Topology Conference 2005Gökova Geometry/Topology Conference, 2006)
      This article consists of loosely related remarks about the geometry of G2-structures on 7-manifolds, some of which are based on unpublished joint work with two other people: F. Reese Harvey and Steven Altschuler. After some ...
    • The origins of spectra, an organization for LGBT mathematicians 

      Bryant, R; Buckmire, R; Khadjavi, L; Lind, D (Notices of the American Mathematical Society, 2019-06-01)