Connected Riemannian Manifolds with Local Isometry

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Theorem

Let $\struct {M, g}$ and $\struct {\tilde M, \tilde g}$ be connected Riemannian manifolds.

Let $\pi : \tilde M \to M$ be a local isometry.


Then $M$ is complete, and $\pi$ is a Riemannian covering map.


Proof




Sources