Vol. 294, No. 1, 2018

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ISSN: 0030-8730
Some Ambrose- and Galloway-type theorems via Bakry–Émery and modified Ricci curvatures

Homare Tadano

Vol. 294 (2018), No. 1, 213–231
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
Authors
Homare Tadano
Department of Mathematics
Graduate School of Science
Osaka University
1-1 Machikaneyama, Toyonaka
Osaka 560-0043
Japan
Department of Mathematics
Faculty of Science Division I
Tokyo University of Science
1-3 Kagurazaka, Shinjuku
Tokyo 162-8601
Japan