The space of Solvsolitons in low dimensions

WILL, CYNTHIA

Norman, OK

Workshop; Workshop on Ricci Solitons and Symmetry; 2012

Univ. de Oklahoma

Up to now, the only known examples of (nontrivial) homogeneous Ricci soliton metrics are the so called solvsolitons; namely, certain left invariant metrics on simply connected solvable Lie groups. In this talk, we will describe the ideas we used to classify the moduli space of solvsolitons of dimension less or equal than 7, up to isometry and scaling. We start with the already known classification of nilsolitons and, by following a characterization given by Lauret, we describe the subspace of solvsolitons associated to a given nilsoliton as the quotient of a Grassmanian by a finite group.