Long-time behavior of awesome homogeneous Ricci flows

Abstract

We show that the set of awesome homogeneous metrics on non-compact manifolds is Ricci flow invariant. Moreover, if the universal cover of such awesome homogeneous space is not contractible the Ricci flow has finite extinction time, confirming the Dynamical Alekseevskii Conjecture in this case. We also analyze the long-time limits of awesome homogeneous Ricci flows.

26 pages. Updated to match the version published in the Pacific Journal of Mathematics

References in corpus (4)

• On Type I Singularities in Ricci flow
• Immortal homogeneous Ricci flows
• Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds
• On the Isometry Group of Immortal Homogeneous Ricci Flows