As on arXiv
Abstract
We study Ricci solitons on the Riemannian manifold equipped with the standard metric. A complete classification of soliton vector fields is obtained: they form a four-dimensional affine space, namely a translate of the Killing algebra . All corresponding solitons are expanding. In addition, gradient solitons are fully characterized and shown to form a one-parameter subfamily of the complete family of soliton fields. As a byproduct, every soliton vector field turns out to be affine, preserving the Levi-Civita connection, the curvature tensor, and the Ricci tensor.
- Submitted
- Aug 20, 2026
- Subjects
- math.DG
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 2021, plus the canon.
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Ricci solitons with an orthogonally intransitive 2-dimensional Abelian Killing algebra
Topics 4-manifolds, Ricci solitons · Shared terms “Killing algebra”, “vector field”, “four dimensional”
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Topics 4-manifolds, Ricci solitons · Shared terms “four dimensional”, “addition”
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Topics 4-manifolds, Ricci solitons · Shared terms “four dimensional”, “addition”
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Topics 4-manifolds, Ricci solitons · Shared terms “curvature tensor”, “four dimensional”
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Topics 4-manifolds, Ricci solitons · Shared terms “four dimensional”, “curvature tensor”
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Topics 4-manifolds, Ricci solitons · Shared terms “four dimensional”, “addition”
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Vanishing bach-like tensors on complete gradient shrinking ricci solitons
Topics 4-manifolds, Ricci solitons
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Topics 4-manifolds, Ricci solitons · Shared terms “four dimensional”
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.