The Manifolds with Ricci Curvature Decay to Zero
Huashui Zhan
DOI: 10.4236/apm.2012.21008   PDF         3,833 Downloads   7,948 Views  


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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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.

Conflicts of Interest

The authors declare no conflicts of interest.


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