Definition:Riemannian Covering
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Definition
Let $\struct {M, g}$ and $\struct {\tilde M, \tilde g}$ be Riemannian manifolds.
Let $\pi : \tilde M \to M$ be a smooth covering map.
Suppose $\pi$ is a local isometry.
Then $\pi$ is called a Riemannian covering.
Sources
- 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Methods for Constructing Riemannian Metrics