As on arXiv
Abstract
It is well known that a unit sphere admits Sasakian 3-structure. Also, Sasakian manifolds are locally isometric to a unit sphere under several curvature and critical conditions. So, a natural question is: Does there exist any curvature or critical condition under which a Sasakian 3-manifold represents a geometrical object other than the unit sphere? In this regard, as an extension of the -Ricci soliton, the notion of -Ricci-Yamabe soliton is introduced and studied on two classes contact metric manifolds. A -dimensional non-Sasakian -contact metric manifold admitting -Ricci-Yamabe soliton is completely classified. Further, it is proved that if a Sasakian 3-manifold admits -Ricci-Yamabe soliton under certain conditions on the soliton vector field , then is -Ricci flat, positive Sasakian and the transverse geometry of is Fano. In addition, the Sasakian 3-metric is homothetic to a Berger sphere and the soliton is steady. Also, the potential vector field is an infinitesimal automorphism of the contact metric structure.
- Submitted
- Aug 24, 2021
- Subjects
- math.DG
Comments: 16 pages
Its neighbourhood
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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-Yamabe solitons on the Lie group
Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Ricci Yamabe”, “Yamabe soliton”, “vector field”
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Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “unit sphere”, “Yamabe soliton”
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Topics Sasakian & contact geometry · Shared terms “metric structure”
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Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Kähler geometry · Shared terms “metric structure”, “vector field”, “automorphisms”
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Topics Sasakian & contact geometry, Almost & η-Ricci solitons, 3-manifolds · Shared terms “soliton vector”, “vector field”, “manifold admitting”
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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 “Ricci Yamabe”, “Yamabe soliton”, “manifold admitting”
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Einstein-type metrics and generalized Ricci solitons on weak -K-contact manifolds
Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci-flat & Calabi–Yau · Shared terms “vector field”
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Kenmotsu metric as conformal -Ricci soliton
Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “vector field”, “potential vector”, “manifold admitting”
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
- 10A.1A Zoo of Three-Manifolds
The 3-sphere, lens spaces, the Poincaré sphere, the Hopf fibration and the shape of space.
- 10A.2Finite Rotation Groups and Spherical Space Forms
Klein's classification by counting poles, the binary groups, and every quotient of the round 3-sphere.
- 10A.4Homotopy Groups, Degree and the Hurewicz Theorem
Spheres mapped into manifolds: the algebraic topology that finite extinction runs on.