On conformally flat manifolds with constant positive scalar curvature

Catino, Giovanni

doi:10.1090/proc/12925

On conformally flat manifolds with constant positive scalar curvature
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by Giovanni Catino

Proc. Amer. Math. Soc. 144 (2016), 2627-2634

DOI: https://doi.org/10.1090/proc/12925

Published electronically: November 4, 2015

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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 Derdzinski metric.

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