As on arXiv
Abstract
Catino, Mastrolia, Monticelli, and Rigoli have launched an ambitious program to study known geometric solitons from a unified perspective, which they term Einstein-type manifolds. This framework allows one to treat Ricci solitons, Yamabe solitons, and all of their generalizations simultaneously. Einstein-type manifolds are characterized by four constants and . In this paper, we show that when , complete gradient Einstein-type Sasakian manifolds are trivial or isometric to the unit sphere. As a consequence, many geometric solitons on Sasakian manifolds turn out to be trivial or isometric to the unit sphere.
Comments: 11 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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Classification of gradient Einstein-type Kähler manifolds with
Topics Almost & η-Ricci solitons, Ricci solitons · Same author Shun Maeta · Shared terms “Einstein type”, “gradient Einstein”, “type manifolds”
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Structure of generalized Yamabe solitons and its applications
Topics Almost & η-Ricci solitons, Ricci solitons · Same author Shun Maeta · Shared terms “Yamabe soliton”, “complete gradient”
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Classification of generalized Yamabe solitons under vanishing conditions on the Weyl, Cotton, and Cao-Chen tensors
Topics Almost & η-Ricci solitons, Ricci solitons · Same author Shun Maeta · Shared terms “gradient Einstein”, “Einstein type”, “Yamabe soliton”
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-Ricci-Yamabe Soliton and Contact Geometry
Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “unit sphere”, “Yamabe soliton”
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Generalized Ricci solitons on LP-Sasakian manifolds admitting the general connection
Topics Sasakian & contact geometry, Ricci solitons
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Sasakian lift of Kaehler manifold and -Sasakian Ricci solitons
Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons
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K-contact manifolds admitting some geometric solitons with Semi-Symmetric Non-Metric Connection
Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “geometric solitons”, “Yamabe soliton”
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Geometry of para-Sasakian metric as an almost conformal -Ricci soliton
Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “Einstein”
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.