As on arXiv
Abstract
We give a result estimating the dimension of the Lie algebra of Killing vector fields on an irreducible non-trivial gradient Ricci soliton. Then we study the structure of this manifold when the maximal dimension is attained. There are local and global implications.
Comments: 18 pages, comments welcome
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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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Kähler-Ricci solitons with almost maximal symmetry
Topics Ricci solitons · Same authors Ha Tuan Dung, Hung Tran · Shared terms “isometry group”, “trivial gradient”, “gradient Ricci”
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Kähler Gradient Ricci Solitons with Large Symmetry
Topics Ricci solitons · Same author Hung Tran · Shared terms “gradient Ricci”, “isometry”, “irreducible”
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Geometry and Analysis of Gradient Ricci Solitons in Dimension Four
Topics Ricci solitons · Same author Hung Tran · Shared terms “gradient Ricci”
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On the Isometry Group of Immortal Homogeneous Ricci Flows
Shared terms “isometry group”
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Infinitesimal maximal symmetry and Ricci soliton solvmanifolds
Topics Ricci solitons · Shared terms “isometry group”, “Lie”
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Ricci solitons of special Lorentzian Lie groups with a four-dimensional isometry group
Topics Ricci solitons · Shared terms “isometry group”, “Lie”
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On Ricci Solitons with Isoparametric Potential Functions
Topics Ricci solitons · Same author Hung Tran · Shared terms “gradient Ricci”
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Rigidity of four-dimensional Kähler-Ricci solitons
Topics Ricci solitons · Same author Hung Tran · Shared terms “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
- 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.