Paper · Jun 20, 2021

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

Sumanjit Sarkar, Santu Dey, Arindam Bhattacharyya

math.DGarXiv:2106.10722
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Abstract

In this paper we study certain types of metrics such as Ricci soliton, -conformal Ricci soliton in 3-dimensional trans-Sasakian manifold. First we have shown that a 3-dimensional trans-Sasakian manifold of type admits a Ricci soliton where the covariant derivative of potential vector field in the direction of unit vector field is orthogonal to . It is also shown that if the structure functions satisfy then the covariant derivative of the potential vector field in the direction of is a constant multiple of . Further, we have evolved the nature of scalar curvature when the manifold satisfies -conformal Ricci soliton of type , provided . Finally, we present an example to verify our findings.

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Submitted
Jun 20, 2021
Subjects
math.DG
Ricci solitonsAlmost & η-Ricci solitons3-manifoldsScalar curvatureSasakian & contact geometry

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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 Sasakian Manifold and *-Ricci Tensor (Venkatesha. and Aruna Kumara H, 2018)8Venkatesha. 2018 *-Conformal η-Ricci Soliton on Sasakian manifold (Soumendu Roy, Santu Dey, Arindam Bhattacharyya et al., 2019)1Roy 2019 Characteristics of almost conformal Ricci solitons on Sasakian manifold (Dipen Ganguly, Nirabhra Basu and Arindam Bhattacharyya, 2021)5Ganguly 2021 *-Conformal η-Ricci soliton within the framework of Kenmotsu manifolds (Sumanjit Sarkar and Santu Dey, 2021)4Sarkar 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)3Mondal 2025 Hyperbolic solitons on trans-Sasakian space forms and its submanifolds (Bidhan Mondal, Sibsankar Panda and Nirabhra Basu, 2026)6Mondal 2026 K-contact manifolds admitting some geometric solitons with Semi-Symmetric Non-Metric Connection (Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya, 2026)7Mondal 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 authors Santu Dey, 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, 3-manifolds · Same authors Sumanjit Sarkar, Santu Dey, Arindam Bhattacharyya · Shared terms “vector field”

  3. 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 author Arindam Bhattacharyya · Shared terms “trans Sasakian”, “conformal Ricci”

  4. -Conformal -Ricci soliton within the framework of Kenmotsu manifolds

    Sumanjit Sarkar and Santu Dey

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

  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 · Same author Arindam Bhattacharyya · Shared terms “conformal Ricci”

  6. Hyperbolic solitons on trans-Sasakian space forms and its submanifolds

    Bidhan Mondal, Sibsankar Panda and Nirabhra Basu

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

  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, Scalar curvature · Same author Arindam Bhattacharyya · Shared terms “conformal Ricci”, “vector field”

  8. Sasakian Manifold and *-Ricci Tensor

    Venkatesha. and Aruna Kumara H

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

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) 3-manifolds Dimension three is where Ricci flow has done its most complete work. It proves geometrization, describes the flow's long-time behaviour, and now… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982) Scalar curvature The trace of the Ricci tensor. Under Ricci flow its minimum never decreases and positive scalar curvature (PSC) is preserved. Start with: On the proof of the positive mass conjecture in general relativity (Schoen et al., 1979)

In the guidebook

  1. 10A.1
    A Zoo of Three-ManifoldsBook 10A · Three-Manifolds and Geometrization

    The 3-sphere, lens spaces, the Poincaré sphere, the Hopf fibration and the shape of space.

  2. 10A.2
    Finite Rotation Groups and Spherical Space FormsBook 10A · Three-Manifolds and Geometrization

    Klein's classification by counting poles, the binary groups, and every quotient of the round 3-sphere.

  3. 10A.4
    Homotopy Groups, Degree and the Hurewicz TheoremBook 10A · Three-Manifolds and Geometrization

    Spheres mapped into manifolds: the algebraic topology that finite extinction runs on.