# On conformally flat manifolds with constant positive scalar curvature

created by catino on 05 Aug 2014
modified on 10 Apr 2016

[BibTeX]

Published Paper

Inserted: 5 aug 2014
Last Updated: 10 apr 2016

Journal: Proc. Amer. Math. Soc.
Volume: 144
Pages: 2627-2634
Year: 2016

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.