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Holonomy and the Lie Algebra of Infinitesimal Motions of A Riemannian Manifold

  • Bertram Kostant
Chapter

Abstract

Let M be a differentiable manifold of class C ?. All tensor fields discussed below are assumed to be of class C ?. Let X be a vector field on M. If X vanishes at a point 0 ? M then X induces, in a natural way, an endomorphism a X of the tangent space V o at 0. In fact if y ? V 0 and Y is any vector field whose value at 0 is y, then define a x y = [X, Y] 0 . It is not hard to see that [X, Y] 0 does not depend on Y so long as the value of Y at 0 is y.

Keywords

Vector Field Riemannian Manifold Mathematical Method Mathematical Society Differential Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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