η- Ricci Solitons on Kenmotsu manifold with Generalized Symmetric Metric Connection

Mohd. Danish Siddiqi; Oğuzhan Bahadır

Paper · Sep 3, 2018

$η$ - Ricci Solitons on Kenmotsu manifold with Generalized Symmetric Metric Connection

Mohd. Danish Siddiqi, Oğuzhan Bahadır

math.DGarXiv:1809.00485

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Abstract

The objective of the present paper is to study the $η$ -Ricci solitons on Kenmotsu manifold with generalized symmetric metric connection of type $(α, β)$ . There are discussed Ricci and $η$ -Ricci solitons with generalized symmetric metric connection of type $(α, β)$ satisfying the conditions $R ˉ . S ˉ = 0$ , $S ˉ . R ˉ = 0$ , $W_{2} ˉ . S ˉ = 0$ and $S ˉ . W_{2} ˉ = 0.$ . Finally, we construct an example of Kenmotsu manifold with generalized symmetric metric connection of type $(α, β)$ admitting $η$ -Ricci solitons.

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Submitted: Sep 3, 2018
Subjects: math.DG
DOI: 10.22190/FUMI2002295S

Comments: arXiv admin note: substantial text overlap with arXiv:1804.10020; text overlap with arXiv:1402.0223 by other authors

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

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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) 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

11B.1
Ricci SolitonsBook 11B · Solitons, Compactness and Singularities
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
12B.2
The Asymptotic Soliton and Three-Dimensional ShrinkersBook 12B · κ-Solutions and Surgery
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.

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

[2] 12B.2
The Asymptotic Soliton and Three-Dimensional ShrinkersBook 12B · κ-Solutions and Surgery
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.

$η$ - Ricci Solitons on Kenmotsu manifold with Generalized Symmetric Metric Connection

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