Homogeneous Ricci Solitons in Low Dimensions

Abstract

In this article, we classify expanding homogeneous Ricci solitons up to dimension 5, according to their presentation as homogeneous spaces. We obtain that they are all isometric to solvsolitons, and this, in particular, implies that the generalized Alekseevskii conjecture holds in these dimensions. In addition, we prove that the conjecture holds in dimension 6 provided the transitive group is not semi-simple.