As on arXiv
Abstract
For each non-flat, unimodular Ricci soliton solvmanifold , we construct a one-parameter family of complete, expanding, gradient Ricci solitons that admit a cohomogeneity one isometric action by . The orbits of this action are hypersurfaces homothetic to . These metrics are asymptotic at one end to an Einstein solvmanifold. In the one-parameter family, exactly one metric is Einstein, and exactly one has orbits that are isometric to .
Comments: 18 pages
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Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Einstein metrics and Killing spinors on pseudo-Riemannian solvmanifolds
Topics Homogeneous spaces, Ricci solitons · Shared terms “Einstein solvmanifold”
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Quaternionic Kähler manifolds fibered by solvsolitons
Topics Homogeneous spaces, Ricci solitons · Shared terms “solvmanifolds”, “unimodular”, “cohomogeneity”
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Expanding Ricci solitons and Higgs bundles
Topics Homogeneous spaces, Ricci solitons · Same author Adam Thompson · Shared terms “Einstein”
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Infinitesimal maximal symmetry and Ricci soliton solvmanifolds
Topics Homogeneous spaces, Ricci solitons · Shared terms “solvmanifolds”, “Einstein”
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Cohomogeneity One Expanding Ricci Solitons and the Expander Degree
Topics Homogeneous spaces, Ricci solitons · Shared terms “parameter family”, “cohomogeneity”
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Classification of superpotentials for cohomogeneity one Ricci solitons
Topics Homogeneous spaces, Ricci solitons · Shared terms “cohomogeneity”, “gradient Ricci”
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Non-Shrinking Ricci Solitons of cohomogeneity one from the quaternionic Hopf fibration
Topics Homogeneous spaces, Ricci solitons · Shared terms “parameter family”, “cohomogeneity”, “Einstein”
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On Ricci Solitons with Isoparametric Potential Functions
Topics Homogeneous spaces, Ricci solitons · Shared terms “cohomogeneity”, “gradient Ricci”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11A.13Homogeneous Flows
A computable laboratory: the flow on Thurston’s geometries.
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
- 12B.2The Asymptotic Soliton and Three-Dimensional Shrinkers
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.