Splitting theorems on complete manifolds with Bakry-Émery curvature

Details Splitting theorems on complete manifolds with Bakry-Émery curvature Splitting theorems on complete manifolds with Bakry-Émery curvature

2011-12-29

arxiv.org/abs/1112.6302v1

Mathematics

Differential Geometry

17 pages

Scientific paper

In this paper we study some splitting properties on complete noncompact
manifolds with smooth measures when $\infty$-dimensional Bakry-\'Emery Ricci
curvature is bounded from below by some negative constant and spectrum of the
weighted Laplacian has a positive lower bound. These results extend the cases
of Ricci curvature and $m$-dimensional Bakry-\'Emery Ricci curvature.

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