Topology of Manifolds with Asymptotically Nonnegative Ricci Curvature

Details Topology of Manifolds with Asymptotically Nonnegative Ricci Curvature Topology of Manifolds with Asymptotically Nonnegative Ricci Curvature

2008-09-26

arxiv.org/abs/0809.4558v1

Mathematics

Differential Geometry

8 pages

Scientific paper

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 R^n 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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