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...)
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Statement

Suppose M and N are complete Riemannian manifolds, and f:M \to N is a local isometry. Then, f is a covering map. In particular, if N is simply connected, then f is an isometry.