Rigidity of complete Riemannian manifolds with vanishing Bach tensor
Bull. Korean Math. Soc.
Published online 2019 Mar 11
Guangyue Huang, and Bingqing Ma
Henan Normal University
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.
Keywords : Sobolev constant, rigidity, vanishing Bach tensor
MSC numbers : Primary 53C24, Secondary 53C21
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