Two rigidity theorems on manifolds with Bakry-Emery Ricci curvature

Two rigidity theorems on manifolds with Bakry-Emery Ricci curvature

Qi-hua Ruan

Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 85, Number 6 (2009), 71-74.

Abstract

In this paper, we generalize the Cheng's maximal diameter theorem and Bishop volume comparison theorem to the manifold with the Bakry-Emery Ricci curvature. As their applications, we obtain some rigidity theorems on the warped product.

Primary Subjects: 53C21

Secondary Subjects: 53C20

Keywords: Maximal diameter; Bakry-Emery Ricci curvature; volume comparison; warped product

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pja/1244037800
Digital Object Identifier: doi:10.3792/pjaa.85.71
Zentralblatt MATH identifier: 05598750
Mathematical Reviews number (MathSciNet): MR2532422

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