Ricci curvature and the topology of open manifolds |
| |
Authors: | Manfredo do Carmo Changyu Xia |
| |
Institution: | (1) Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110 Jardim Botanico, 22460-320 Rio de Janeiro, RJ - Brasil, e-mail: manfredo@impa.br , BR |
| |
Abstract: | In this paper, we prove that an open Riemannian n-manifold with Ricci curvature and for some is diffeomorphic to a Euclidean n-space if the volume growth of geodesic balls around p is not too far from that of the balls in . We also prove that a complete n-manifold M with is diffeomorphic to if , where is the volume of unit ball in .
Received 5 May, 1997 |
| |
Keywords: | Mathematics Subject Classification (1991): 53C20 53C42 |
本文献已被 SpringerLink 等数据库收录! |