Splitting theorems on complete manifolds with Bakry-Émery curvature

Abstract

In this paper we study some splitting properties on complete noncompact manifolds with smooth measures when $\infty$-dimensional Bakry-Émery 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-Émery Ricci curvature.

17 pages

References in corpus (1)

• A note on the splitting theorem for the weighted measure

Cited by in corpus (1)

• A note on the splitting theorem for the weighted measure