On conformally flat manifolds with constant positive scalar curvature
On conformally flat manifolds with constant positive scalar curvature
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.