As on arXiv
Abstract
In the paper, we study complete almost Ricci solitons using the concepts and methods of geometric dynamics and geometric analysis. In particular, we characterize Einstein manifolds in the class of complete almost Ricci solitons. Then, we examine compact almost Ricci solitons using the orthogonal expansion of the Ricci tensor, this allows us to substantiate the concept of almost Ricci solitons.
Comments: 8 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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New applications of the Ahlfors Laplacian
Topics Almost & η-Ricci solitons, Ricci solitons · Same authors Sergey Stepanov, Irina Tsyganok · Shared terms “orthogonal expansion”, “compact almost”, “Ricci tensor”
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Almost Ricci solitons on Finsler spaces
Topics Almost & η-Ricci solitons, Einstein metrics, Ricci solitons
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--Ricci solitons and Einstein metrics on a weak -Kenmotsu manifold
Topics Almost & η-Ricci solitons, Einstein metrics, Ricci solitons · Same author Vladimir Rovenski · Shared terms “Ricci tensor”
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--Ricci solitons on weak Kenmotsu -manifolds
Topics Almost & η-Ricci solitons, Einstein metrics, Ricci solitons · Same author Vladimir Rovenski · Shared terms “Ricci tensor”
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On conformal collineation and almost Ricci solitons
Topics Almost & η-Ricci solitons, Ricci solitons
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Characterizations of Almost Ricci Bourguignon Solitons
Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “compact almost”, “Einstein”
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-Ricci solitons and -Einstein metrics on weak -Kenmotsu -manifolds
Topics Almost & η-Ricci solitons, Einstein metrics, Ricci solitons · Same author Vladimir Rovenski
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On a compact Einstein-type manifolds with Riemannian foliations
Topics Almost & η-Ricci solitons, Einstein metrics, Ricci solitons · Shared terms “compact almost”
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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.