As on arXiv
Abstract
We study the setting of 2-step nilpotent Lie groups in the particular case that its type (p,q) is not exceptional. We demonstrate that, generically, the orbits of in are congruent even when a Ricci soliton metric does exists. In doing so, we provide a counterexample to the local version of a conjecture of Taketomi-Tamaru.
- Submitted
- Oct 18, 2018
- Last revised
- Jan 1, 2025 (v2)
- Subjects
- math.DG
Comments: Substantial revision. Explicit example constructed and included. 11 pages
Its neighbourhood
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 2016, plus the canon.
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Einstein solvmanifolds as submanifolds of symmetric spaces
Topics Homogeneous spaces, Ricci solitons · Same author Michael Jablonski · Shared terms “Tamaru”, “step nilpotent”, “Lie groups”
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A Hilbert–Mumford criterion for nilsolitons
Topics Homogeneous spaces, Ricci solitons · Shared terms “Taketomi”, “Tamaru”, “nilpotent Lie”
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Maximal Symmetry and Unimodular Solvmanifolds
Topics Homogeneous spaces, Ricci solitons · Same author Michael Jablonski · Shared terms “Lie groups”
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Infinitesimal maximal symmetry and Ricci soliton solvmanifolds
Topics Homogeneous spaces, Ricci solitons · Same author Michael Jablonski · Shared terms “Lie groups”
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Nilpotent Lie algebras obtained by ordered sets and Ricci solitons
Topics Homogeneous spaces, Ricci solitons · Shared terms “nilpotent Lie”, “Tamaru”, “step nilpotent”
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Positive Hermitian curvature flow on complex 2-step nilpotent Lie groups
Topics Homogeneous spaces · Shared terms “step nilpotent”, “nilpotent Lie”, “Lie groups”
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Positive Hermitian curvature flow on 2-step nilpotent Lie groups
Topics Homogeneous spaces · Shared terms “step nilpotent”, “nilpotent Lie”, “Lie groups”
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Sectional Curvature Pinching of Two-Step Nilmanifolds
Topics Homogeneous spaces, Ricci solitons · Shared terms “step nilpotent”, “nilpotent Lie”, “Lie groups”
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.