Author(s)

Huashui Zhan

.

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.

Cheeger-Gromoll Theorem; Busemann Function; Complete Riemannian Manifold; Ricci Curvature Decay to Zero

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.