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Topological rigidity theorems for open Riemannian manifolds

✍ Scribed by Qiaoling Wang; Changyu Xia

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
127 KB
Volume
279
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

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. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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