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 ... 
Recent advances in the theory of holonomy
Bryant, R (Asterisque, 20001201)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 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)