Difference between revisions of "Open Riemannian manifold"

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==Definition==
 
==Definition==
  
A [[Riemannian manifold]] is said to be '''open'''' if it can be embedded as an open subset of Euclidean space in such a way that the Riemannian metric on the manifold is simply the restriction to the manifold of the usual metric on Euclidean space.
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A [[Riemannian manifold]] is said to be '''open'''' if it is not compact.

Revision as of 01:59, 7 July 2007

This article defines a property that makes sense for a Riemannian metric over a differential manifold

Definition

A Riemannian manifold is said to be open' if it is not compact.