Diffeomorphic theorems for open Riemannian manifolds with curvature decay

作者：Wu Chuanxi^*; Xie Zhiqi; Li Guanghan

来源：Publicationes Mathematicae-Debrecen, 2011, 79(1-2): 133-144.

DOI：10.5486/PMD.2011.4971

• Open manifolds
• curvature decay
• large volume growth

In this paper, we study the topology of complete non-compact Riemannian manifolds with curvature decay to a non-positive constant. We show that such a complete open manifold M is diffeomorphic to a Euclidean n-space R-n if it contains enough rays starting from the base point. As applications, we also show that this kind of manifolds with Ricci curvature bounded from below by a non-positive constant are diffeomorphic to R-n if the volumes of geodesic balls in M grow properly. Our results generalize the main theorems of Wang-Xia for manifolds with quadratic curvature decay to zero.

• 出版日期2011-7
• 单位湖北大学