Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SOME RIGIDITY CHARACTERIZATIONS OF EINSTEIN METRICS AS CRITICAL POINTS FOR QUADRATIC CURVATURE FUNCTIONALS

  • Huang, Guangyue (College of Mathematics and Information Science Henan Normal University) ;
  • Ma, Bingqing (College of Mathematics and Information Science Henan Normal University) ;
  • Yang, Jie (College of Mathematics and System Science Xinjiang University)
  • Received : 2019.11.21
  • Accepted : 2020.03.25
  • Published : 2020.11.30
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Abstract

We study rigidity results for the Einstein metrics as the critical points of a family of known quadratic curvature functionals involving the scalar curvature, the Ricci curvature and the Riemannian curvature tensor, characterized by some pointwise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moreover, we also provide a few rigidity results for locally conformally flat critical metrics.

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References

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