Rigidity of Riemannian manifolds with positive scalar curvature

Guangyue Huang

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arXiv · 1707.00902

Rigidity of Riemannian manifolds with positive scalar curvature

Guangyue Huang

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Abstract

For the Bach-flat closed manifold with positive scalar curvature, we prove a rigidity result under a given inequality involving the Weyl curvature and the traceless Ricci curvature. Moveover, under an inequality involving $L^{\frac{n}{2}}$-norm of the Weyl curvature, the traceless Ricci curvature and the Yamabe invariant, we also provide a similar rigidity result. As an application, we obtain some rigidity results on 4-dimensional manifolds.

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Guangyue Huang. 2017-07-04. Rigidity of Riemannian manifolds with positive scalar curvature. https://arxiv.org/abs/1707.00902

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