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The Manifolds with Ricci Curvature Decay to Zero
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Advances in Pure Mathematics·Volume 02 (2012)·Pages 36–38·Published 6 January 2012·DOI10.4236/apm.2012.21008
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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.
KeywordsCheeger-Gromoll TheoremBusemann FunctionComplete Riemannian ManifoldRicci Curvature Decay to Zero
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