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.
Fei Yang and Liangdi Zhang
China University of Geosciences, China University of Geosciences
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
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