The space of solvsolitons in low dimensions

Abstract

Up to now, the only known examples of homogeneous nontrivial Ricci soliton metrics are the so called solvsolitons, i.e. certain left invariant metrics on simple connected solvable Lie groups. In this paper, we describe the moduli space of solvsolitons of dimension less or equal than 6 up to isomorphism and scaling. We start with the already known classification of nilsolitons and, following the characterization given by Lauret in a recent article, we describe the subspace of solvsolitons associated to a given nilsoliton, as the quotient of a Grassmanian by a finite group.