The Ricci flow on solvmanifolds of real type

Abstract

We show that for any solvable Lie group of real type, any homogeneous Ricci flow solution converges in Cheeger-Gromov topology to a unique non-flat solvsoliton, which is independent of the initial left-invariant metric. As an application, we obtain results on the isometry groups of non-flat solvsoliton metrics and Einstein solvmanifolds.

18 pages; v2: improved exposition, proofs of main results simplified, appendices are now contained in arXiv:1701.00628v3