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http://dx.doi.org/10.4134/BKMS.b160319

RIGIDITY OF GRADIENT SHRINKING AND EXPANDING RICCI SOLITONS  

Yang, Fei (School of Mathematics and Physics China University of Geosciences)
Zhang, Liangdi (School of Mathematics and Physics China University of Geosciences)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.3, 2017 , pp. 817-824 More about this Journal
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;
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