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Topological rigidity theorems for open Riemannian manifolds
Author(s) -
Wang Qiaoling,
Xia Changyu
Publication year - 2006
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310395
Subject(s) - mathematics , sectional curvature , diffeomorphism , ricci curvature , manifold (fluid mechanics) , riemannian manifold , geodesic , pure mathematics , rigidity (electromagnetism) , ricci flat manifold , topology (electrical circuits) , euclidean space , curvature , scalar curvature , curvature of riemannian manifolds , base (topology) , mathematical analysis , combinatorics , geometry , physics , mechanical engineering , quantum mechanics , engineering
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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