As on arXiv
Abstract
In this article, we study Ricci-Yamabe solitons on the Lie group equipped with a natural left-invariant Riemannian metric, explicitly determining the vector fields that characterize them. We then deduce that, in the case of a Ricci soliton, it is expanding, whereas in the case of a Yamabe soliton, it is shrinking. Finally, we show that if this Lie group is a gradient Ricci-Yamabe soliton, the vector field belongs to , and we explicitly provide the Perelman potential.
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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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Ricci Solitons, Almost Theta-Yamabe Solitons, and Finite-Order Tensor Symmetries of a Vector Field on Riemannian Manifolds with Rank-One Anisotropic Curvature
Topics Almost & η-Ricci solitons, Ricci solitons · Same authors Abdou Bousso, Ameth Ndiaye · Shared terms “Yamabe soliton”, “vector field”, “determining”
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Geometric study of non-constant vector fields making hyperbolic space Ricci-Bourguignon solitons
Topics Almost & η-Ricci solitons · Same authors Abdou Bousso, Ameth Ndiaye · Shared terms “vector field”, “characterize”
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Ricci Solitons on the Poincaré upper half plane
Topics Almost & η-Ricci solitons, Ricci solitons · Same authors Abdou Bousso, Ameth Ndiaye · Shared terms “characterize”
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Structure of generalized Yamabe solitons and its applications
Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Yamabe soliton”, “Perelman”
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-Ricci-Yamabe Soliton and Contact Geometry
Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Ricci Yamabe”, “Yamabe soliton”, “vector field”
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Ricci Solitons on the Lie Group and Applications
Topics Homogeneous spaces, Ricci solitons · Shared terms “Lie groups”, “invariant Riemannian”, “left invariant”
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Hyperbolic Ricci Solitons on the Unit Tangent Bundle of the Hyperbolic Strip
Topics Almost & η-Ricci solitons, Ricci solitons · Same author Ameth Ndiaye · Shared terms “Lie”, “left invariant”, “vector field”
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Ricci Solitons of Left-Invariant Metrics on Lie Groups with Derived Algebra of Dimension at Most Two
Topics Homogeneous spaces, Ricci solitons · Shared terms “Lie groups”, “left invariant”, “invariant Riemannian”
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.