Paper · May 1, 2020

-contact metric as -conformal Ricci soliton

Dibakar Dey, Pradip Majhi

math.DGarXiv:2005.02194
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Abstract

The aim of this paper is characterize a class of contact metric manifolds admitting -conformal Ricci soliton. It is shown that if a -dimensional -contact metric manifold admits -conformal Ricci soliton or -conformal gradient Ricci soliton, then the manifold M is -Ricci at and locally isometric to the Riemannian of a flat -dimensional manifold and an -dimensional manifold of constant curvature 4 for and flat for . Further, for the first case, the soliton vector field is conformal and for the -gradient case, the potential function is either harmonic or satisfy a Poisson equation. Finally, an example is presented to support the results.

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Submitted
May 1, 2020
Subjects
math.DG

Comments: 9 pages. arXiv admin note: text overlap with arXiv:2004.13405

Ricci solitonsAlmost & η-Ricci solitonsSasakian & contact geometry

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  1. -Ricci-Yamabe Soliton and Contact Geometry

    Dibakar Dey

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Same author Dibakar Dey · Shared terms “locally isometric”, “soliton vector”, “manifold admitting”

  2. Remarks on Riemann and Ricci solitons in -contact metric manifolds

    Adara M. Blaga and Dan Radu Latcu

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “vector field”

  3. On non-gradient -quasi-Einstein contact metric manifolds

    Dhriti Sundar Patra and Vladimir Rovenski

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “locally isometric”, “constant curvature”, “vector field”

  4. The k-almost Ricci solitons and contact geometry

    Amalendu Ghosh and Dhriti Sundar Patra

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “vector field”, “gradient Ricci”

  5. Characteristics of almost conformal Ricci solitons on Sasakian manifold

    Dipen Ganguly, Nirabhra Basu and Arindam Bhattacharyya

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “conformal Ricci”, “conformal gradient”, “potential function”

  6. Kenmotsu metric as conformal -Ricci soliton

    Dipen Ganguly

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “manifold admitting”, “vector field”, “characterize”

  7. K-contact manifolds admitting some geometric solitons with Semi-Symmetric Non-Metric Connection

    Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “conformal Ricci”, “manifold admitting”, “vector field”

  8. *-Conformal η-Ricci Soliton on Sasakian manifold

    Soumendu Roy, Santu Dey, Arindam Bhattacharyya et al.

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “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.

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

  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.