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On complete manifolds with nonnegative Ricci curvature. (English) Zbl 0704.53032

By a well known theorem of Cheeger and Gromoll, a complete open Riemannian manifold M of nonnegative sectional curvature contains a totally convex, compact submanifold S such that M is diffeomorphic to the normal bundle of S. In particular, M has finite topological type. This is not true if only nonnegative Ricci curvature is assumed, as shown by examples of Sha and Yang. The authors establish, on the other hand, that if M has diameter growth of order \(o(r^{1/n})\) and the sectional curvature is bounded away from -\(\infty\), then M is homotopy equivalent to the interior of a compact manifold with boundary.
Reviewer: W.Ballmann

MSC:

53C20 Global Riemannian geometry, including pinching
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