Browsing by Author "0110365"
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A solution of a problem of Sophus Lie: Normal forms of twodimensional metrics admitting two projective vector fields
Bryant, Robert; Manno, G; Matveev, VS (Mathematische Annalen, 20080201)We give a complete list of normal forms for the twodimensional metrics that admit a transitive Lie pseudogroup of geodesicpreserving transformations and we show that these normal forms are mutually nonisometric. This ... 
An introduction to Lie groups and symplectic geometry
Bryant, Robert (Geometry and quantum field theory (Park City, UT, 1991)IAS/Park City Mathematics Series, 1995) 
Bochnerkähler metrics
Bryant, Robert (Journal of the American Mathematical Society, 20010701) 
Calibrated Embeddings in the Special Lagrangian and Coassociative Cases
Bryant, Robert (Annals of Global Analysis and Geometry, 20001201)Every closed, oriented, real analytic Riemannian 3manifold can be isometrically embedded as a special Lagrangian submanifold of a CalabiYau 3fold, even as the real locus of an antiholomorphic, isometric involution. Every ... 
Calibrated embeddings in the special Lagrangian and coassociative cases
Bryant, Robert (Annals of Global Analysis and Geometry, 2000)Every closed, oriented, real analytic Riemannian 3manifold can be isometrically embedded as a special Lagrangian submanifold of a CalabiYau 3fold, even as the real locus of an antiholomorphic, isometric involution. Every ... 
Complex analysis and a class of Weingarten surfaces
Bryant, Robert (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 ... 
Conformal geometry and 3plane fields on 6manifolds
Bryant, Robert (RIMS Kokyuroku, 200607) 
Dbranes and Spinc structures
Bryant, Robert; Sharpe, E (Physics Letters, Section B: Nuclear, Elementary Particle and HighEnergy Physics, 19991201)It was recently pointed out by E. Witten that for a Dbrane to consistently wrap a submanifold of some manifold, the normal bundle must admit a Spinc structure. We examine this constraint in the case of type II ... 
Exterior Differential Systems and EulerLagrange Partial Differential Equations
Bryant, Robert; Griffiths, Phillip A; Grossman, DAWe use methods from exterior differential systems (EDS) to develop a geometric theory of scalar, firstorder Lagrangian functionals and their associated EulerLagrange PDEs, subject to contact transformations. The first ... 
Élie Cartan and geometric duality
Bryant, Robert (Journées Élie Cartan 1998 et 1999, 2000) 
Geodesic behavior for Finsler metrics of constant positive flag curvature on $S^2$
Bryant, Robert; Foulon, P; Ivanov, S; Matveev, VS; Ziller, W (20171101)We 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, Robert (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 ... 
Gradient Kahler Ricci solitons
Bryant, Robert (Asterisque, 20081001)Some observations about the local and global generality of gradient Kahler Ricci solitons are made, including the existence of a canonically associated holomorphic volume form and vector field, the local generality of solutions ... 
Harmonic morphisms with fibers of dimension one
Bryant, Robert (Communications in Analysis and Geometry, 20000401)The harmonic morphisms φ : Mn+1 → Nn are studied using the methods of the moving frame and exterior differential systems and three main results are achieved. The first result is a local structure theorem for such maps in ... 
Holonomy and Special Geometries
Bryant, Robert (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, Robert; 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. 
Leviflat Minimal Hypersurfaces in Twodimensional Complex Space Forms
Bryant, RobertThe purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Leviflat and minimal. The main results are as follows: When the curvature of the complex space form is ... 
Metrisability of twodimensional projective structures
Bryant, Robert; 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 ... 
NonEmbedding and NonExtension Results in Special Holonomy
Bryant, Robert (The Many Facets of Geometry: A Tribute to Nigel Hitchin, 20100901)© Oxford University Press 2010. All rights reserved.In the early analyses of metrics with special holonomy in dimensions 7 and 8, particularly in regards to their existence and generality, heavy use was made of the CartanKähler ... 
Notes on exterior differential systems
Bryant, Robert (20140513)These are notes for a very rapid introduction to the basics of exterior differential systems and their connection with what is now known as Lie theory, together with some typical and notsotypical applications to illustrate ...