The Ricci flow on solvmanifolds of real type

TL;DR

This paper proves that homogeneous Ricci flows on solvable Lie groups of real type always converge to a unique solvsoliton, regardless of initial metrics, with implications for isometry groups and Einstein solvmanifolds.

Contribution

It establishes the convergence of Ricci flows on solvmanifolds of real type to a unique solvsoliton, advancing understanding of geometric evolution on these spaces.

Findings

Ricci flow solutions converge to a unique solvsoliton

Convergence is independent of initial metrics

Results on isometry groups and Einstein solvmanifolds

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.