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The Manifolds with Ricci Curvature Decay to Zero

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Author(s): Huashui Zhan

Journal: Advances in Pure Mathematics
ISSN 2160-0368

Volume: 02;
Issue: 01;
Start page: 36;
Date: 2012;
Original page

Keywords: Cheeger-Gromoll Theorem | Busemann Function | Complete Riemannian Manifold | Ricci Curvature Decay to Zero

ABSTRACT
The paper quotes the concept of Ricci curvature decay to zero. Base on this new concept, by modifying the proof of the canonical Cheeger-Gromoll Splitting Theorem, the paper proves that for a complete non-compact Riemannian manifold M with Ricci curvature decay to zero, if there is a line in M, then the isometrically splitting M = R × N is true.
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