Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2016.04.13
  • Published : 2017.05.31
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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.

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References

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