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

In: Collected Papers

Author

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  • Bertram Kostant

    (Massachusetts Institute of Technology, Department of Mathematics)

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.

Suggested Citation

  • Bertram Kostant, 2009. "Holonomy and the Lie Algebra of Infinitesimal Motions of A Riemannian Manifold," Springer Books, in: Anthony Joseph & Shrawan Kumar & Michèle Vergne (ed.), Collected Papers, pages 1-15, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-09583-7_1
    DOI: 10.1007/b94535_1
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