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 APM  Vol.2 No.1 , January 2012
The Manifolds with Ricci Curvature Decay to Zero
Huashui Zhan
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.
Keywords: Cheeger-Gromoll Theorem; Busemann Function; Complete Riemannian Manifold; Ricci Curvature Decay to Zero
Cite this paper: H. Zhan, "The Manifolds with Ricci Curvature Decay to Zero," Advances in Pure Mathematics, Vol. 2 No. 1, 2012, pp. 36-38. doi: 10.4236/apm.2012.21008.
References

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