Open Riemannian manifold: Difference between revisions

Revision as of 01:59, 7 July 2007

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

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

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