As on arXiv
Abstract
In this paper, we revisit the study of almost Ricci-Bourguignon solitons by clarifying their position in the broader context of Einstein-type metrics. Motivated by known rigidity results for compact almost Ricci solitons, we aim to identify conditions under which a compact almost RB-soliton is trivial or exhibits special geometric properties. We compare our results with classical theorems of Barros and Ribeiro, and explain explicitly how our work extends or complements these earlier findings.
Comments: 21 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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Geometric study of non-constant vector fields making hyperbolic space Ricci-Bourguignon solitons
Topics Almost & η-Ricci solitons · Shared terms “Bourguignon soliton”, “Ricci Bourguignon”
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Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Bourguignon soliton”, “Ricci Bourguignon”
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Back to almost Ricci solitons
Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “compact almost”, “Einstein”
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Topics Almost & η-Ricci solitons, Stability & uniqueness, Ricci solitons · Shared terms “characterization”, “Einstein”
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Topics Almost & η-Ricci solitons, Ricci solitons
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On a compact Einstein-type manifolds with Riemannian foliations
Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Einstein type”, “compact almost”
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Non-compact Ricci Solitons of Finite Volume with Potential Field of Constant Length
Topics Ricci solitons · Same authors Mohammad Aqib, Hemangi Madhusudan Shah
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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.