On conformally flat manifolds with constant positive scalar curvature

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 Derdziński metric.

Cited by in corpus (2)

• On compact manifolds with harmonic curvature and positive scalar curvature
• Some $L^p$ rigidity results for complete manifolds with harmonic curvature