Topology of Manifolds with Asymptotically Nonnegative Ricci Curvature
Abstract
In this paper, we study the topology of complete noncompact Riemannian manifolds with asymptotically nonnegative Ricci curvature. We show that a complete noncompact manifold with asymptoticaly nonnegative Ricci curvature and sectional curvature decay at most quadratically is diffeomorphic to a Euclidean n-space Rn under some conditions on the density of rays starting from the base point p or on the volume growth of geodesic balls in M.
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