Myers' type theorem with the Bakry-Émery Ricci tensor

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-Émery 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.

A reference added, minor typos corrected. Accepted by Ann. Glob. Anal. Geom