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A Characterization of Invariant Affine Connections

In: Collected Papers

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  • Bertram Kostant

    (Massachusetts Institute of Technology, Department of Mathematics)

Abstract

In [1] Ambrose and Singer gave a necessary and sufficient condition (Theorem 3 here) for a simply connected complete Riemannian manifold to admit a transitive group of motions. Here we shall give a simple proof of a more general theorem—Theorem 1 (the proof of Theorem 1 became suggestive to us after we noted that the T x of [1] is just the a x of [6] when X is restricted to p 0, see [6], p. 539). In fact after introducing, below, the notion of one affine connection A on a manifold being rigid with respect to another affine connection B on M and making some observations concerning such a relationship, Theorem 1 is seen to be a reformulation of Theorem 2.

Suggested Citation

  • Bertram Kostant, 2009. "A Characterization of Invariant Affine Connections," Springer Books, in: Anthony Joseph & Shrawan Kumar & Michèle Vergne (ed.), Collected Papers, pages 190-205, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-09583-7_12
    DOI: 10.1007/b94535_12
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