A Myers Theorem for Bakry--Emery Ricci tensor and a New Diameter Estimate

Sanghun Lee, Seungsu Hwang

Published 2019-04-18Version 1

Using a generalization of the Myers Theorem and the Bakry--Emery Ricci tensor, we prove three theorems which are related to the Myers compactness thoerem. In particular, our second theorem is sharper than that obtained by Cavalcante, Oliveira, and Santos. In addition, in the third theorem we find a weaker condition on $f'(t)$ than that obtained by Soylu.