Now showing items 1-20 of 20

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

      Bryant, RL; 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 ...
    • Bochner-kähler metrics 

      Bryant, RL (Journal of the American Mathematical Society, 2001-07-01)
    • Calibrated embeddings in the special Lagrangian and coassociative cases 

      Bryant, RL (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 ...
    • Calibrated Embeddings in the Special Lagrangian and Coassociative Cases 

      Bryant, RL (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 ...
    • D-branes and Spinc structures 

      Sharpe, E; Bryant, RL (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 ...
    • Geodesic behavior for Finsler metrics of constant positive flag curvature on $S^2$ 

      Bryant, RL; Foulon, P; Ivanov, SV; 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, ...
    • Gradient Kahler Ricci solitons 

      Bryant, RL (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 ...
    • Non-Embedding and Non-Extension Results in Special Holonomy 

      Bryant, RL (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, RL (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 ...
    • On Finsler surfaces of constant flag curvature with a Killing field 

      Bryant, RL; Huang, L; Mo, X (Journal of Geometry and Physics, 2017-06-01)
      © 2017 Elsevier B.V. We study two-dimensional Finsler metrics of constant flag curvature and show that such Finsler metrics that admit a Killing field can be written in a normal form that depends on two arbitrary functions ...
    • On the conformal volume of 2-tori 

      Bryant, RL (2015-07-06)
      This note provides a proof of a 1985 conjecture of Montiel and Ros about the conformal volume of tori. (This material is not really new; I'm making it available now because of requests related to recent interest ...
    • On the convex Pfaff-Darboux Theorem of Ekeland and Nirenberg 

      Bryant, RL (2015-12-22)
      The classical Pfaff-Darboux Theorem, which provides local `normal forms' for 1-forms on manifolds, has applications in the theory of certain economic models. However, the normal forms needed in these models come with an ...
    • Projectively flat finsler 2-spheres of constant curvature 

      Bryant, RL (Selecta Mathematica, New Series, 1997-12-01)
      After recalling the structure equations of Finsler structures on surfaces, I define a notion of "generalized Finsler structure" as a way of microlocalizing the problem of describing Finsler structures subject to curvature ...
    • Real hypersurfaces in unimodular complex surfaces 

      Bryant, RL (2004-07-27)
      A unimodular complex surface is a complex 2-manifold X endowed with a holomorphic volume form. A strictly pseudoconvex real hypersurface M in X inherits not only a CR-structure but a canonical coframing as well. In this ...
    • Recent advances in the theory of holonomy 

      Bryant, RL (Asterisque, 2000-12-01)
      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 ...
    • Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces 

      Bryant, RL (2001-03-05)
      I use local differential geometric techniques to prove that the algebraic cycles in certain extremal homology classes in Hermitian symmetric spaces are either rigid (i.e., deformable only by ambient motions) or quasi-rigid ...
    • S.-S. Chern's study of almost-complex structures on the six-sphere 

      Bryant, RL (2014-05-14)
      In 2003, S.-s. Chern began a study of almost-complex structures on the 6-sphere, with the idea of exploiting the special properties of its well-known almost-complex structure invariant under the exceptional group $G_2$. ...
    • SO(n)-Invariant special Lagrangian submanifolds of ℂ n+1 with fixed loci 

      Bryant, RL (Chinese Annals of Mathematics. Series B, 2006-01-01)
      Let SO(n) act in the standard way on ℂn and extend this action in the usual way to ℂn+1 = ℂ ⊕ ℂ n . It is shown that a nonsingular special Lagrangian submanifold L ⊂ ℂn+1 that is invariant under this SO(n)-action intersects ...
    • Some differential complexes within and beyond parabolic geometry 

      Bryant, RL; Eastwood, MG; Gover, AR; Neusser, K (2012-03-19)
      For smooth manifolds equipped with various geometric structures, we construct complexes that replace the de Rham complex in providing an alternative fine resolution of the sheaf of locally constant functions. In case that ...
    • Some examples of special Lagrangian Tori 

      Bryant, RL (Advances in Theoretical and Mathematical Physics, 1999-01-01)