International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 39, Pages 2085-2090
doi:10.1155/S0161171204211188
On the structure of Riemannian manifolds of almost nonnegative Ricci curvature
Department of Mathematics, Myong Ji University, San 38-2, Namdong, Kyunggi, Yongin 449-728, Korea
Received 14 November 2002
Copyright © 2004 Gabjin Yun. 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 study the structure of manifolds with almost nonnegative Ricci curvature. We prove a compact Riemannian manifold with bounded curvature, diameter bounded from above, and Ricci curvature bounded from below by an almost nonnegative real number such that the first Betti number havingcodimension two is an infranilmanifold or a finite cover is a sphere bundle over a torus. Furthermore, if we assume the Ricci curvature is bounded and volume is bounded from below, then the manifold must be an infranilmanifold.