Paper · Jun 20, 2021

-Conformal -Ricci soliton within the framework of Kenmotsu manifolds

Sumanjit Sarkar, Santu Dey

math.DGarXiv:2106.10632
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Abstract

The goal of our present paper is to deliberate -conformal -Ricci soliton within the framework of Kenmotsu manifolds. Here we have shown that a Kenmotsu metric as a -conformal -Ricci soliton is Einstein metric if the soliton vector field is contact. Further, we have evolved the characterization of the Kenmotsu manifold or the nature of the potential vector field when the manifold satisfies gradient almost -conformal -Ricci soliton. Next, we have contrived -conformal -Ricci soliton admitting -almost Kenmotsu manifold and proved that the manifold is Ricci flat and is locally isometric to . Finally we have constructed some examples to illustrate the existence of -conformal -Ricci soliton, gradient almost -conformal -Ricci soliton on Kenmotsu manifold and -almost Kenmotsu manifolds.

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Submitted
Jun 20, 2021
Subjects
math.DG
Ricci solitonsEinstein metricsRicci-flat & Calabi–YauAlmost & η-Ricci solitonsSasakian & contact geometry

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.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper A note on Ricci soliton in almost Kenmotsu manifold (Fatemah Mofarreh and U. C. De, 2018)4Mofarreh 2018 *-Ricci solitons and gradient almost *-Ricci solitons on Kenmotsu manifolds (Venkatesha Venkatesh, Devaraja Mallesha Naik and H Aruna Kumara, 2019)6Venkatesh 2019 Geometric solitons in a D-homothetically deformed Kenmotsu manifold (Adara M. Blaga, 2020)8Blaga 2020 Almost η-Ricci solitons on Kenmotsu manifolds (Dhriti Sundar Patra and Vladimir Rovenski, 2020)2Patra 2020 Geometry of almost contact metrics as almost *-Ricci solitons (Dhriti Sundar Patra, Akram Ali and Fatemah Mofarreh, 2021)7Patra 2021 Ricci solitons and certain related metrics on 3-dimensional trans-Sasakian manifold (Sumanjit Sarkar, Santu Dey and Arindam Bhattacharyya, 2021)5Sarkar 2021 Kenmotsu metric as conformal η-Ricci soliton (Dipen Ganguly, 2021)1Ganguly 2021 Geometry of para-Sasakian metric as an almost conformal η-Ricci soliton (Sumanjit Sarkar, Santu Dey and Arindam Bhattacharyya, 2021)3Sarkar 2021
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Kenmotsu metric as conformal -Ricci soliton

    Dipen Ganguly

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

  2. Almost -Ricci solitons on Kenmotsu manifolds

    Dhriti Sundar Patra and Vladimir Rovenski

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Einstein metrics · Shared terms “Kenmotsu manifold”, “gradient almost”, “Kenmotsu metric”

  3. Geometry of para-Sasakian metric as an almost conformal -Ricci soliton

    Sumanjit Sarkar, Santu Dey and Arindam Bhattacharyya

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Einstein metrics · Same authors Sumanjit Sarkar, Santu Dey · Shared terms “soliton vector”, “gradient almost”, “vector field”

  4. A note on Ricci soliton in almost Kenmotsu manifold

    Fatemah Mofarreh and U. C. De

    Topics Sasakian & contact geometry, Ricci solitons · Shared terms “Kenmotsu manifold”, “almost Kenmotsu”, “potential vector”

  5. Ricci solitons and certain related metrics on 3-dimensional trans-Sasakian manifold

    Sumanjit Sarkar, Santu Dey and Arindam Bhattacharyya

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Same authors Sumanjit Sarkar, Santu Dey · Shared terms “manifold satisfies”, “potential vector”, “vector field”

  6. -Ricci solitons and gradient almost -Ricci solitons on Kenmotsu manifolds

    Venkatesha Venkatesh, Devaraja Mallesha Naik and H Aruna Kumara

    Topics Sasakian & contact geometry, Ricci solitons · Shared terms “Kenmotsu manifold”, “gradient almost”, “vector field”

  7. Geometry of almost contact metrics as almost -Ricci solitons

    Dhriti Sundar Patra, Akram Ali and Fatemah Mofarreh

    Topics Sasakian & contact geometry, Einstein metrics, Ricci solitons · Shared terms “Kenmotsu”, “vector field”, “potential vector”

  8. Geometric solitons in a -homothetically deformed Kenmotsu manifold

    Adara M. Blaga

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

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) Einstein metrics Metrics whose Ricci curvature is a constant multiple of the metric. They are the fixed points of normalised Ricci flow, and the most natural metrics… Start with: On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I (Yau, 1978) Ricci-flat & Calabi–Yau Ricci-flat metrics do not move under Ricci flow. Every known compact simply connected example has special holonomy (Calabi–Yau, hyperkähler, G₂… Start with: On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I (Yau, 1978) 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.