• Title/Summary/Keyword: B56

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RIGIDITY OF COMPLETE RIEMANNIAN MANIFOLDS WITH VANISHING BACH TENSOR

  • Huang, Guangyue;Ma, Bingqing
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.5
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    • pp.1341-1353
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    • 2019
  • 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.