Myers' type theorem with the Bakry-\'Emery Ricci tensor
Differential Geometry
2018-05-16 v2
Abstract
In this paper we prove a new Myers' type diameter estimate on a complete connected Reimannian manifold which admits a bounded vector field such that the Bakry-\'Emery Ricci tensor has a positive lower bound. The result is sharper than previous Myers' type results. The proof uses the generalized mean curvature comparison applied to the excess function instead of the classical second variation of geodesics.
Keywords
Cite
@article{arxiv.1706.07897,
title = {Myers' type theorem with the Bakry-\'Emery Ricci tensor},
author = {Jia-Yong Wu},
journal= {arXiv preprint arXiv:1706.07897},
year = {2018}
}
Comments
A reference added, minor typos corrected. Accepted by Ann. Glob. Anal. Geom