Rigidity of gradient shrinking and expanding Ricci solitons
Bull. Korean Math. Soc. 2017 Vol. 54, No. 3, 817-824
https://doi.org/10.4134/BKMS.b160319
Published online May 31, 2017
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
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