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has been cited by the following article:
TITLE: The Manifolds with Ricci Curvature Decay to Zero
AUTHORS: Huashui Zhan
KEYWORDS: Cheeger-Gromoll Theorem; Busemann Function; Complete Riemannian Manifold; Ricci Curvature Decay to Zero
JOURNAL NAME: Advances in Pure Mathematics, Vol.2 No.1, January 6, 2012
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.