Table of Contents
Geometry
Volume 2013, Article ID 235436, 4 pages
http://dx.doi.org/10.1155/2013/235436
Research Article

The Long-Time Behavior of the Ricci Tensor under the Ricci Flow

Department of Mathematics, University of California-Berkeley, Berkeley, CA 94720-3840, USA

Received 17 June 2013; Accepted 19 August 2013

Academic Editor: Giovanni Calvaruso

Copyright © 2013 Christian Hilaire. 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 show that, given an immortal solution to the Ricci flow on a closed manifold with uniformly bounded curvature and diameter, the Ricci tensor goes to zero as . We also show that if there exists an immortal solution on a closed 3-dimensional manifold such that the product of the curvature and the square of the diameter is uniformly bounded, then this solution must be of type III.