As on arXiv
Abstract
In this paper, we study solitons on -dimensional manifolds. In particular, we show that -dimensional pseudo-symmetric gradient Ricci solitons and nontrivial gradient Yamabe solitons are locally isometric to either , , , or .
- Submitted
- Jun 17, 2016
- Subjects
- math.DG
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 2016, plus the canon.
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Structure of generalized Yamabe solitons and its applications
Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “gradient Yamabe”, “Yamabe soliton”
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Investigations on a Riemannian manifold with a semi-symmetric non-metric connection and gradient solitons
Topics Almost & η-Ricci solitons, 3-manifolds, Ricci solitons · Shared terms “gradient Yamabe”, “Yamabe soliton”, “gradient Ricci”
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Ricci-Yamabe solitons on the Lie group
Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Yamabe soliton”, “gradient Ricci”
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-Ricci-Yamabe Soliton on Riemannian Submersions from Riemannian manifolds
Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Yamabe soliton”
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-contact metric as -conformal Ricci soliton
Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “dimensional manifolds”, “locally isometric”, “gradient Ricci”
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-Ricci-Yamabe Soliton and Contact Geometry
Topics Almost & η-Ricci solitons, 3-manifolds, Ricci solitons · Shared terms “Yamabe soliton”, “locally isometric”
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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 · Shared terms “Yamabe soliton”, “gradient Yamabe”, “nontrivial”
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Three-dimensional Ricci-degenerate Riemannian manifolds satisfying geometric equations
Topics Almost & η-Ricci solitons, 3-manifolds, Ricci solitons · Shared terms “gradient Ricci”
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.