Connected Riemannian Manifolds with Local Isometry/Corollary

Theorem

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

Let $\pi : \tilde M \to M$ be a Riemannian covering map.

Then $M$ is complete if and only if $\tilde M$ complete.

Proof

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Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 6$: Geodesics and Distance. Completeness