Some Ambrose- and Galloway-type theorems via Bakry–Émery and modified Ricci curvatures

Homare Tadano

Vol. 294 (2018), No. 1, 213–231

DOI: 10.2140/pjm.2018.294.213

Abstract

We establish some compactness theorems of Ambrose- and Galloway-type for complete Riemannian manifolds in the context of the Bakry–Émery and modified Ricci curvatures. Our compactness theorems generalize previous ones obtained by Fernández-López and García-Río, Wei and Wylie, and Limoncu, Rimoldi, and Zhang.

Keywords

Myers-type theorem, Ambrose-type theorem, Galloway-type theorem, smooth metric measure space, Bakry–Émery Ricci curvature, modified Ricci curvature

Mathematical Subject Classification 2010

Primary: 53C21

Secondary: 53C20

Milestones

Received: 8 April 2016

Revised: 8 June 2017

Accepted: 5 October 2017

Published: 5 January 2018