Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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RIGIDITY OF COMPLETE RIEMANNIAN MANIFOLDS WITH VANISHING BACH TENSOR

  • Huang, Guangyue (Department of Mathematics Henan Normal University) ;
  • Ma, Bingqing (Department of Mathematics Henan Normal University)
  • Received : 2018.12.07
  • Accepted : 2019.02.07
  • Published : 2019.09.30
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Abstract

For complete Riemannian manifolds with vanishing Bach tensor and positive constant scalar curvature, we provide a rigidity theorem characterized by some pointwise inequalities. Furthermore, we prove some rigidity results under an inequality involving $L^{\frac{n}{2}}$-norm of the Weyl curvature, the traceless Ricci curvature and the Sobolev constant.

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References

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