The space of solsolitons in low dimensions

Abstract

Up to now, the only known examples of homogeneous nontrivial Ricci soliton metrics are the so called solsolitons, i.e. certain left invariant metrics on simple connected solvable Lie groups. In this paper, we describe the moduli space of solsolitons 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, we describe the subspace of solsolitons associated to a given nilsoliton, as the quotient of a Grassmanian by a finite group.