Paper · Apr 10, 2021

Characteristics of almost conformal Ricci solitons on Sasakian manifold

Dipen Ganguly, Nirabhra Basu, Arindam Bhattacharyya

math.DGarXiv:2104.04801
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Abstract

In this paper, we characterize the potential function of the almost conformal gradient Ricci soliton on a Sasakian manifold in terms of the non-dynamical scalar field and deduce the necessary condition for the potential function to be constant. Furthermore, a relation between and the potential function has been established. Finally, we prove a sufficient condition for an almost conformal Ricci soliton to be an almost conformal gradient Ricci soliton and also a characterization of the soliton in terms of shrinking, steady or expanding has been done.

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Submitted
Apr 10, 2021
Subjects
math.DG, math-ph

Comments: 12 pages

Ricci solitonsAlmost & η-Ricci solitonsSasakian & contact geometry

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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 *-Conformal η-Ricci Soliton on Sasakian manifold (Soumendu Roy, Santu Dey, Arindam Bhattacharyya et al., 2019)1Roy 2019 N(k)-contact metric as ∗-conformal Ricci soliton (Dibakar Dey and Pradip Majhi, 2020)7Dey 2020 Characteristics of conformal Ricci soliton on warped product spaces (Dipen Ganguly, Nirabhra Basu and Arindam Bhattacharyya, 2021)3Ganguly 2021 Ricci solitons and certain related metrics on 3-dimensional trans-Sasakian manifold (Sumanjit Sarkar, Santu Dey and Arindam Bhattacharyya, 2021)6Sarkar 2021 Kenmotsu metric as conformal η-Ricci soliton (Dipen Ganguly, 2021)8Ganguly 2021 Geometry of para-Sasakian metric as an almost conformal η-Ricci soliton (Sumanjit Sarkar, Santu Dey and Arindam Bhattacharyya, 2021)2Sarkar 2021 Curvature tensors and hyperbolic solitons on Lorentzian trans-Sasakian space form (Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya, 2025)5Mondal 2025 K-contact manifolds admitting some geometric solitons with Semi-Symmetric Non-Metric Connection (Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya, 2026)4Mondal 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. *-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 · Same author Arindam Bhattacharyya

  2. 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, Ricci solitons · Same author Arindam Bhattacharyya · Shared terms “almost conformal”, “characteristics”

  3. Characteristics of conformal Ricci soliton on warped product spaces

    Dipen Ganguly, Nirabhra Basu and Arindam Bhattacharyya

    Topics Almost & η-Ricci solitons, Ricci solitons · Same authors Dipen Ganguly, Nirabhra Basu, Arindam Bhattacharyya · Shared terms “conformal Ricci”, “characteristics”, “characterization”

  4. 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 · Same authors Nirabhra Basu, Arindam Bhattacharyya · Shared terms “conformal Ricci”, “sufficient conditions”, “necessary”

  5. Curvature tensors and hyperbolic solitons on Lorentzian trans-Sasakian space form

    Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Same authors Nirabhra Basu, Arindam Bhattacharyya · Shared terms “conformal Ricci”

  6. 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 author Arindam Bhattacharyya · Shared terms “conformal Ricci”

  7. -contact metric as -conformal Ricci soliton

    Dibakar Dey and Pradip Majhi

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

  8. Kenmotsu metric as conformal -Ricci soliton

    Dipen Ganguly

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Same author Dipen Ganguly · Shared terms “relation”, “characterize”

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.