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The space of solvsolitons in low dimensions

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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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Authors and Affiliations

  1. CIEM and FaMAF, Universidad Nacional de Córdoba, 5000, Córdoba, Argentina

    Cynthia Will

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  1. Cynthia Will
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Correspondence to Cynthia Will.

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Will, C. The space of solvsolitons in low dimensions. Ann Glob Anal Geom 40, 291–309 (2011). https://doi.org/10.1007/s10455-011-9258-0

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  • DOI: https://doi.org/10.1007/s10455-011-9258-0

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