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arXiv · 1707.05036

Rigidity of complete Riemannian manifolds with vanishing Bach tensor

Bingqing Ma·Guangyue Huang
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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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Bingqing Ma, Guangyue Huang. 2017-07-17. Rigidity of complete Riemannian manifolds with vanishing Bach tensor. https://doi.org/10.1016/j.geomphys.2017.11.004

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