Collected Papers pp 190-205 | Cite as

# A Characterization of Invariant Affine Connections

## 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.

## Keywords

Riemannian Manifold Mathematical Method Differential Geometry Topological Group Simple Proof## Preview

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## References

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