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arXiv · 1408.0902

On conformally flat manifolds with constant positive scalar curvature

Giovanni Catino
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Abstract

We classify compact conformally flat $n$-dimensional manifolds with constant positive scalar curvature and satisfying an optimal integral pinching condition: they are covered isometrically by either $\mathbb{S}^{n}$ with the round metric, $\mathbb{S}^{1}\times \mathbb{S}^{n-1}$ with the product metric or $\mathbb{S}^{1}\times \mathbb{S}^{n-1}$ with a rotationally symmetric Derdzi\'nski metric.

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Giovanni Catino. 2014-08-05. On conformally flat manifolds with constant positive scalar curvature. https://arxiv.org/abs/1408.0902

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