Geometric solitons in a D-homothetically deformed Kenmotsu manifold

Adara M. Blaga

Paper · Aug 8, 2020

Geometric solitons in a $D$ -homothetically deformed Kenmotsu manifold

Adara M. Blaga

math.DGarXiv:2008.03502v4

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Abstract

We consider almost Riemann and almost Ricci solitons in a $D$ -homothetically deformed Kenmotsu manifold having as potential vector field a gradient vector field, a solenoidal vector field or the Reeb vector field of the deformed structure, and explicitly obtain the Ricci and scalar curvatures for some cases. We also provide a lower bound for the Ricci curvature of the initial Kenmotsu manifold when the deformed manifold admits a gradient almost Riemann or almost Ricci soliton.

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Submitted: Aug 8, 2020
Last revised: Jan 15, 2021 (v4)
Subjects: math.DG
Journal: Filomat 36(1), 175-186 (2022)

Ricci solitons Almost & η-Ricci solitons Scalar curvature Sasakian & contact geometry

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Almost $η$ -Ricci solitons on Kenmotsu manifolds
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Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Scalar curvature · Shared terms “Kenmotsu manifold”, “Reeb vector”, “vector field”
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Dipen Ganguly2021

Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “Kenmotsu manifold”, “vector field”, “Reeb vector”
Remarks on almost Riemann solitons with gradient or torse-forming vector field
Adara M. Blaga2020

Topics Almost & η-Ricci solitons, Ricci solitons · Same author Adara M. Blaga · Shared terms “almost Riemann”, “vector field”, “gradient vector”
$*$ -Conformal $η$ -Ricci soliton within the framework of Kenmotsu manifolds
Sumanjit Sarkar and Santu Dey2021

Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “Kenmotsu manifold”, “gradient almost”, “vector field”
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Venkatesha Venkatesh, Devaraja Mallesha Naik and H Aruna Kumara2019

Topics Sasakian & contact geometry, Ricci solitons · Shared terms “Kenmotsu manifold”, “gradient almost”, “vector field”
A note on Ricci soliton in almost Kenmotsu manifold
Fatemah Mofarreh and U. C. De2018

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Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Same author Adara M. Blaga · Shared terms “vector field”, “potential vector”

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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.

Ricci solitons Metrics that change under Ricci flow only by scaling and diffeomorphisms: shrinking, steady or expanding solitons. Start with: The Ricci flow on surfaces (Hamilton, 1988) Almost & η-Ricci solitons Variations on the Ricci soliton equation: let the constant λ become a function (almost solitons), add a term along a contact form (η-Ricci… Start with: Ricci almost solitons (Pigola et al., 2010) Scalar curvature The trace of the Ricci tensor. Under Ricci flow its minimum never decreases and positive scalar curvature (PSC) is preserved. Start with: On the proof of the positive mass conjecture in general relativity (Schoen et al., 1979) Sasakian & contact geometry Sasakian manifolds are odd-dimensional manifolds whose metric cone is Kähler. They carry a transverse Kähler structure, so Kähler–Ricci flow has an… Start with: THE SASAKI–RICCI FLOW (SMOCZYK et al., 2010)

In the guidebook

6C.4
The Yamabe Problem and Critical ExponentsBook 6C · Nonlinear PDE: Variational and Geometric Methods
Conformal changes of scalar curvature, the Yamabe functional, Aubin's threshold and Schoen's solution, concentration compactness and bubbles, and why Perelman's log-Sobolev minimisers always exist.
9B.6
Scalar Curvature and TopologyBook 9B · Comparison, Convergence and Heat on Manifolds
Positive scalar curvature, its obstructions, and the positive mass theorem.
11B.1
Ricci SolitonsBook 11B · Solitons, Compactness and Singularities
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.

[1] 6C.4
The Yamabe Problem and Critical ExponentsBook 6C · Nonlinear PDE: Variational and Geometric Methods
Conformal changes of scalar curvature, the Yamabe functional, Aubin's threshold and Schoen's solution, concentration compactness and bubbles, and why Perelman's log-Sobolev minimisers always exist.

[2] 9B.6
Scalar Curvature and TopologyBook 9B · Comparison, Convergence and Heat on Manifolds
Positive scalar curvature, its obstructions, and the positive mass theorem.

[3] 11B.1
Ricci SolitonsBook 11B · Solitons, Compactness and Singularities
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.

Geometric solitons in a $D$ -homothetically deformed Kenmotsu manifold

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