Soul theorem: Difference between revisions

Revision as of 01:38, 7 July 2007

Any open Riemannian manifold $(M,g)$ with nonnegative sectional curvature contains a compact totally geodesic submanifold $S$ (called the soul), such that $M$ is diffeomorphic to the normal bundle on $S$ , viz $\nu (S)$ .

Improving the metric in an open manifold with nonnegative curvature by Luis Guijarro, Proceedings of the American Mathematical Society, Volume 126, Number 5, May 1998, Pages 1541-1545

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	==External links==		==External links==

	* [http://www.ams.org/proc/1998-126-05/S0002-9939-98-04287-7/S0002-9939-98-04287-7.pdf ''Improving the metric in an open manifold with nonnegative curvature'']		* [http://www.ams.org/proc/1998-126-05/S0002-9939-98-04287-7/S0002-9939-98-04287-7.pdf Improving the metric in an open manifold with nonnegative curvature]