On compact Riemannian manifolds with harmonic weyl curvature

Haiping Fu; Huiya He

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arXiv · 1810.06301

On compact Riemannian manifolds with harmonic weyl curvature

Haiping Fu·Huiya He

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Abstract

We give some rigidity theorems for an n$(\geq4)$-dimensional compact Riemannian manifold with harmonic Weyl curvature, positive scalar curvature and positive constant $\sigma_2$. Moreover, when $n=4,$ we prove that a 4-dimensional compact locally conformally flat Riemannian manifold with positive scalar curvature and positive constant $\sigma_2$ is isometric to a quotient of the round $\mathbb{S}^4$.

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BibTeX RIS

Haiping Fu, Huiya He. 2018-10-15. On compact Riemannian manifolds with harmonic weyl curvature. https://arxiv.org/abs/1810.06301

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