Browsing by Author "Bryant, R"
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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 (20110527)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, WWe study nonreversible 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 1parameter family. In particular, ... 
Geodesically reversible Finsler 2spheres of constant curvature
Bryant, R (Inspired by S. S. ChernA 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 (20110111)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 twodimensional projective structures
Bryant, R; Dunajski, M; Eastwood, M (Journal of Differential Geometry, 20091201)We carry out the programme of R. Liouville [19] to construct an explicit local obstruction to the existence of a LeviCivita 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 ... 
PseudoReimannian metrics with parallel spinor fields and vanishing Ricci tensor
Bryant, R (Global analysis and harmonic analysis (MarseilleLuminy, 1999)Séminaires et Congrès, 2000)I discuss geometry and normal forms for pseudoRiemannian 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 G2structures
Bryant, R (Proceedings of Gökova GeometryTopology Conference 2005Gökova Geometry/Topology Conference, 2006)This article consists of loosely related remarks about the geometry of G2structures on 7manifolds, 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, 20190601)