On locally conformally flat manifolds with positive pinched Ricci curvature

Abstract

By using the Yamabe flow, we prove that if $(M^n,g)$, $n\ge 3$, is an $n$-dimensional locally conformally flat complete Riemannian manifold $Rc\ge \epsilon Rg>0$, where $\epsilon >0$ is a uniformly constant, then $M^n$ must be compact. Our result shows that Hamilton's pinching conjecture also holds for higher dimensional case if we assume additionally the metric is locally conformally flat.

to appear in Calc. Var. Partial Differ