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.