Topological rigidity theorems for open Riemannian manifolds

In this article, we study topology of complete non-compact Riemannian manifolds. We show that a complete open manifold with quadratic curvature decay is diffeomorphic to a Euclidean n-space R-n if it contains enough rays starting from the base point. We also show that a complete non-compact n-dimensional Riemannian manifold M with nonnegative Ricci curvature and quadratic curvature decay is diffeomorphic to R-n if the volumes of geodesic balls in M grow properly. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.