On the long time behavior of homogeneous Ricci flows

  • Christoph Böhm

    Universität Münster, Germany

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.

Cite this article

Christoph Böhm, On the long time behavior of homogeneous Ricci flows. Comment. Math. Helv. 90 (2015), no. 3, pp. 543–571

DOI 10.4171/CMH/364