Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2017; 54(3): 817-824

Online first article January 4, 2017      Printed May 31, 2017

https://doi.org/10.4134/BKMS.b160319

Copyright © The Korean Mathematical Society.

Rigidity of gradient shrinking and expanding Ricci solitons

Fei Yang and Liangdi Zhang

China University of Geosciences, China University of Geosciences

Abstract

In this paper, we prove that a gradient shrinking Ricci soliton is rigid if the radial curvature vanishes and the second order divergence of Bach tensor is non-positive. Moreover, we show that a complete non-compact gradient expanding Ricci soliton is rigid if the radial curvature vanishes, the Ricci curvature is nonnegative and the second order divergence of Bach tensor is nonnegative.

Keywords: rigidity, gradient Ricci soliton, Bach tensor

MSC numbers: 53C25, 53C24