Homogeneous Ricci solitons in low dimensions

TL;DR

This paper classifies low-dimensional expanding homogeneous Ricci solitons, showing they are all solvsolitons and confirming the generalized Alekseevskii conjecture in dimensions up to 6 under certain conditions.

Contribution

It provides a complete classification of expanding homogeneous Ricci solitons in dimensions up to 6 and verifies the conjecture in these cases.

Findings

All such solitons in dimensions ≤5 are isometric to solvsolitons.

The generalized Alekseevskii conjecture holds in these dimensions.

The conjecture also holds in dimension 6 if the transitive group is not semisimple.

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 semisimple.