As on arXiv
Abstract
We provide conditions for a Riemannian manifold with a nontrivial closed affine conformal Killing vector field to be isometric to a Euclidean sphere or to the Euclidean space. Also, we formulate some triviality results for almost Ricci solitons with affine conformal Killing potential vector field.
Comments: 13 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 2021, plus the canon.
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On some -dimensional almost -Ricci solitons with diagonal metrics
Topics Almost & η-Ricci solitons, Ricci solitons · Same author Adara M. Blaga · Shared terms “potential vector”, “vector field”
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Ricci solitons and curvature inheritance on Robinson-Trautman spacetimes
Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “collineation”
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Almost Ricci solitons on Finsler spaces
Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “vector field”, “nontrivial”
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Back to almost Ricci solitons
Topics Almost & η-Ricci solitons, Ricci solitons
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Clairaut conformal submersions from Ricci solitons
Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “vector field”, “Killing vector”
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Characterizations of Almost Ricci Bourguignon Solitons
Topics Almost & η-Ricci solitons, Ricci solitons
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Almost Ricci Solitons on Class Hypersurfaces of Product Spaces
Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “vector field”, “potential vector”
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Solitons on Statistical Manifolds and Their Submanifolds
Topics Almost & η-Ricci solitons, Ricci solitons · Same author Bang-Yen Chen · Shared terms “vector field”, “Riemannian manifolds”
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.