Yamabe flow and the Myers-type theorem on complete manifolds

Abstract

In this paper,we prove the following Myers-type theorem: if $(M^n,g)$, $n\geq 3$, is an n-dimensional complete locally conformally flat Riemannian manifold with bounded Ricci curvature satisfying the Ricci pinching condition $Rc\geq \epsilon Rg>0$, where $\epsilon>0$ is an uniform constant, then $M^n$ must be compact.