On locally conformally flat manifolds with positive pinched Ricci curvature

Liang Cheng

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arXiv · 2303.06648

On locally conformally flat manifolds with positive pinched Ricci curvature

Liang Cheng

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Abstract

By using the Yamabe flow, we prove that if $(M^n,g)$, $n\geq3$, is an $n$-dimensional locally conformally flat complete Riemannian manifold $Rc\geq \epsilon Rg>0$, where $\epsilon>0$ is a uniformly constant, then $M^n$ must be compact. Our result shows that Hamilton's pinching conjecture also holds for higher dimensional case if we assume additionally the metric is locally conformally flat.

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Liang Cheng. 2023-03-12. On locally conformally flat manifolds with positive pinched Ricci curvature. https://arxiv.org/abs/2303.06648

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