Paper · Apr 23, 2020

-Ricci-Yamabe Soliton on Riemannian Submersions from Riemannian manifolds

Mohd. Danish Siddiqi, Mehmet Akif Akyol

math.DGarXiv:2004.14124
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Abstract

In this research article, we establish the geometrical bearing on Riemannian submersions in terms of -Ricci-Yamabe Soliton with the potential field and giving the classification of any fiber of Riemannian submersion is an -Ricci-Yamabe soliton, -Ricci soliton and -Yamabe soliton. We also discuss the various conditions for which the target manifold of Riemannian submersion is an -Ricci-Yamabe soliton, -Ricci soliton, -Yamabe soliton and quasi-Yamabe soliton. In a particular case when the potential filed of the -Ricci-Yamabe soliton is of gradient type, we derive a Laplacian equation and providing some examples of an -Ricci-Yamabe soliton on a Riemannian submersion. Finally, we study harmonic aspect of -Ricci-Yamabe soliton on Riemannian submersions and mention geometrical and physical effects of Ricci-Yamabe solitons.

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Submitted
Apr 23, 2020
Subjects
math.DG

Comments: 16 pages. arXiv admin note: text overlap with arXiv:1404.2385, arXiv:1311.1676 by other authors

Ricci solitonsAlmost & η-Ricci solitons

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  1. Riemannian Submersions Whose Total Manifolds Admitting a Ricci Soliton

    Şemsi Eken Meriç and Erol Kılıç

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Riemannian submersion”, “target manifold”

  2. Ricci-Yamabe solitons on the Lie group

    Abdou Bousso and Ameth Ndiaye

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Ricci Yamabe”, “Yamabe soliton”

  3. Solitonic aspects of submanifolds in Kenmotsu statistical manifolds

    Mohd. Danish Siddiqi and Aliya Naaz Siddiqui

    Topics Almost & η-Ricci solitons, Ricci solitons · Same author Mohd. Danish Siddiqi · Shared terms “Yamabe soliton”, “quasi Yamabe”, “research”

  4. Structure of generalized Yamabe solitons and its applications

    Shun Maeta

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Yamabe soliton”, “research”

  5. -Ricci-Yamabe Soliton and Contact Geometry

    Dibakar Dey

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Ricci Yamabe”, “Yamabe soliton”, “geometrical”

  6. Conformal Submersions Whose Total Manifolds Admit a Ricci Soliton

    Kiran Meena and Akhilesh Yadav

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “submersion”, “Riemannian manifold”

  7. - Ricci Solitons on Kenmotsu manifold with Generalized Symmetric Metric Connection

    Mohd. Danish Siddiqi and Oğuzhan Bahadır

    Topics Almost & η-Ricci solitons, Ricci solitons · Same author Mohd. Danish Siddiqi

  8. Special solitons on 3-manifolds

    Nasrin Malekzadeh and Esmaiel Abedi

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “Yamabe soliton”

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.

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)

In the guidebook

  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.