The space of solvsolitons in low dimensions

Author： Will Cynthia  

Publisher： Springer Publishing Company

ISSN： 0232-704X

Source： Annals of Global Analysis and Geometry, Vol.40, Iss.3, 2011-10, pp. : 291-309

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Abstract

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.

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