The space of solvsolitons in low dimensions

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 article, we describe the moduli space of solvsolitons of dimension ≤ 6 up to isomorphism and scaling. We start with the already known classification of nilsolitons and, following the characterization given by Lauret in (J. Reine Angew. Math. 650:1–21, 2011), we describe the subspace of solvsolitons associated to a given nilsoliton, as the quotient of a Grassmanian by a finite group.