# Local isometry of complete Riemannian manifolds is covering map

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Revision as of 13:06, 22 May 2008 by Vipul (talk | contribs) (New page: ==Statement== Suppose <math>M</math> and <math>N</math> are complete Riemannian manifolds, and <math>f:M \to N</math> is a local isometry. Then, <math>f</math> is a [[covering map...)

## Statement

Suppose and are complete Riemannian manifolds, and is a local isometry. Then, is a covering map. In particular, if is simply connected, then is an isometry.