Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Improving the metric in an open manifold
with nonnegative curvature

Author: Luis Guijarro
Journal: Proc. Amer. Math. Soc. 126 (1998), 1541-1545
MSC (1991): Primary 53C20
MathSciNet review: 1443388
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The soul theorem states that any open Riemannian manifold $(\!M\!,\!g\!)$ with nonnegative sectional curvature contains a totally geodesic compact submanifold $S$ such that $M$ is diffeomorphic to the normal bundle of $S$. In this paper we show how to modify $g$ into a new metric $g'$ so that:

  1. $g'$ has nonnegative sectional curvature and soul $S$.
  2. The normal exponential map of $S$ is a diffeomorphism.
  3. $(M,g')$ splits as a product outside of a compact set.
As a corollary we obtain that any such $M$ is diffeomorphic to the interior of a convex set in a compact manifold with nonnegative sectional curvature.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53C20

Retrieve articles in all journals with MSC (1991): 53C20

Additional Information

Luis Guijarro
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104

PII: S 0002-9939(98)04287-7
Received by editor(s): October 25, 1996
Communicated by: Christopher Croke
Article copyright: © Copyright 1998 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia