On the long time behavior of homogeneous Ricci flows

Abstract

In this paper we prove the following structure results for homogeneous Ricci flow solutions: Any homogeneous Ricci flow solution with finite extinction time develops a Type I singularity. Any homogeneous Ricci flow solution on a compact homogeneous space, not diffeomorphic to a torus, has finite extinction time. Any immortal homogeneous Ricci flow solution develops a Type III singularity and the natural blow downs subconverge to an immortal locally homogeneous Ricci flow solution.