Now showing items 1-12 of 12

    • 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 ...
    • 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)