Rigidity of complete Riemannian manifolds with vanishing Bach tensor
Bull. Korean Math. Soc. 2019 Vol. 56, No. 5, 1341-1353
https://doi.org/10.4134/BKMS.b181193
Published online September 30, 2019
Guangyue Huang, Bingqing Ma
Henan Normal University; 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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