Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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RIGIDITY CHARACTERIZATION OF COMPACT RICCI SOLITONS

  • Li, Fengjiang (Department of Mathematics East China Normal University) ;
  • Zhou, Jian (Department of Mathematics Yunnan Normal University)
  • Received : 2018.11.02
  • Accepted : 2018.11.29
  • Published : 2019.11.01
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Abstract

In this paper, we firstly define the Ricci mean value along the gradient vector field of the Ricci potential function and show that it is non-negative on a compact Ricci soliton. Furthermore a Ricci soliton is Einstein if and only if its Ricci mean value is vanishing. Finally, we obtain a compact Ricci soliton $(M^n,g)(n{\geq}3)$ is Einstein if its Weyl curvature tensor and the Kulkarni-Nomizu product of Ricci curvature are orthogonal.

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References

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