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

  • Bertram KostantEmail author


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.


Vector Field Riemannian Manifold Mathematical Method Mathematical Society Differential Geometry 
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© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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