A general convergence result for the Ricci flow in higher dimensions

Abstract

Let $(M,g_0)$ be a compact Riemannian manifold of dimension $n\ge 4$. We show that the normalized Ricci flow deforms $g_0$ to a constant curvature metric, provided that $(M,g_0)\times \mathbb{R}$ has positive isotropic curvature. This condition is stronger than two-positive flag curvature but weaker than two-positive curvature operator