Myers’ type theorem with the Bakry–Émery Ricci tensor

• Published in: Annals of global analysis and geometry Vol. 54; no. 4; pp. 541 - 549
• Main Author: Wu, Jia-Yong
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.12.2018; Springer Nature B.V
• Subjects: Analysis; Curvature; Differential Geometry; Geodesy; Geometry; Global Analysis and Analysis on Manifolds; Lower bounds; Mathematical Physics; Mathematics; Mathematics and Statistics; Secondary 53C20; Ricci soliton; Myers’ theorem; Bakry–Émery Ricci curvature; Primary 53C25; 53C21

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...