Now showing items 1-20 of 39

    • A solution of a problem of Sophus Lie: Normal forms of two-dimensional metrics admitting two projective vector fields 

      Bryant, Robert; Manno, G; Matveev, VS (Mathematische Annalen, 2008-02-01)
      We give a complete list of normal forms for the two-dimensional metrics that admit a transitive Lie pseudogroup of geodesic-preserving transformations and we show that these normal forms are mutually non-isometric. 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)
    • Bochner-kähler metrics 

      Bryant, Robert (Journal of the American Mathematical Society, 2001-07-01)
    • Calibrated Embeddings in the Special Lagrangian and Coassociative Cases 

      Bryant, Robert (Annals of Global Analysis and Geometry, 2000-12-01)
      Every closed, oriented, real analytic Riemannian 3-manifold can be isometrically embedded as a special Lagrangian submanifold of a Calabi-Yau 3-fold, 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 3-manifold can be isometrically embedded as a special Lagrangian submanifold of a Calabi-Yau 3-fold, even as the real locus of an antiholomorphic, isometric involution. Every ...
    • Complex analysis and a class of Weingarten surfaces 

      Bryant, Robert (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 ...
    • Conformal geometry and 3-plane fields on 6-manifolds 

      Bryant, Robert (RIMS Kokyuroku, 2006-07)
    • D-branes and Spinc structures 

      Bryant, Robert; Sharpe, E (Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 1999-12-01)
      It was recently pointed out by E. Witten that for a D-brane 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 Euler-Lagrange Partial Differential Equations 

      Bryant, Robert; Griffiths, Phillip A; Grossman, DA
      We use methods from exterior differential systems (EDS) to develop a geometric theory of scalar, first-order Lagrangian functionals and their associated Euler-Lagrange 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 (2017-11-01)
      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, Robert (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 ...
    • Gradient Kahler Ricci solitons 

      Bryant, Robert (Asterisque, 2008-10-01)
      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, 2000-04-01)
      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 (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.
    • Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms 

      Bryant, Robert
      The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is ...
    • Metrisability of two-dimensional projective structures 

      Bryant, Robert; 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 ...
    • Non-Embedding and Non-Extension Results in Special Holonomy 

      Bryant, Robert (The Many Facets of Geometry: A Tribute to Nigel Hitchin, 2010-09-01)
      © 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 Cartan-Kähler ...
    • Notes on exterior differential systems 

      Bryant, Robert (2014-05-13)
      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 not-so-typical applications to illustrate ...