Table of Contents
Geometry
Volume 2013, Article ID 694169, 12 pages
http://dx.doi.org/10.1155/2013/694169
Research Article

Metric Ricci Curvature for Manifolds

1Department of Computer Science, SUNY at Stony Brook, NY 11794-4400, USA
2Department of Mathematics, Technion, 32000 Haifa, Israel
3Department of Mathematics and Computer Science, The Open University, 53537 Ra’anana, Israel

Received 30 April 2013; Accepted 28 July 2013

Academic Editor: Bennett Palmer

Copyright © 2013 David Xianfeng Gu and Emil Saucan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce a metric notion of Ricci curvature for manifolds and study its convergence properties. We also prove a fitting version of the Bonnet-Myers theorem, for surfaces as well as for a large class of higher dimensional manifolds.