Paper · Sep 3, 2019

*-Conformal η-Ricci Soliton on Sasakian manifold

Soumendu Roy, Santu Dey, Arindam Bhattacharyya, Shyamal Kumar Hui

math.DGarXiv:1909.01318
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Abstract

In this paper we study *-Conformal η-Ricci soliton on Sasakian manifolds. Here, we discuss some curvature properties on Sasakian manifold admitting *-Conformal η-Ricci soliton. We obtain some significant results on *-Conformal η-Ricci soliton in Sasakian manifolds satisfying R(ξ,X).S = 0, S(ξ,X).R = 0, {\overline}P(ξ,X).S = 0, where {\overline}P is Pseudo-projective curvature tensor.The conditions for *-Conformal η-Ricci soliton on Φ-conharmonically flat and Φ-projectively flat Sasakian manifolds have been obtained in this article. Lastly we give an example of 5-dimensional Sasakian manifolds satisfying *-Conformal η-Ricci soliton.

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Submitted
Sep 3, 2019
Subjects
math.DG
Journal
2021
DOI
10.1142/S1793557122500358

Comments: 15 pages

Ricci solitonsAlmost & η-Ricci solitonsSasakian & contact geometry

Its neighbourhood

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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 Invariant and anti-invariant submanifolds of special quasi-sasakian manifolds (Shyamal Kumar Hui and Joydeb Roy, 2017)8Hui 2017 Remarks on almost η-Ricci solitons in (ε)-para Sasakian manifolds (Adara M. Blaga and Selcen Yuksel Perktas, 2018)6Blaga 2018 Sasakian Manifold and *-Ricci Tensor (Venkatesha. and Aruna Kumara H, 2018)4Venkatesha. 2018 Characteristics of almost conformal Ricci solitons on Sasakian manifold (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)1Sarkar 2021 Geometry of para-Sasakian metric as an almost conformal η-Ricci soliton (Sumanjit Sarkar, Santu Dey and Arindam Bhattacharyya, 2021)2Sarkar 2021 Generalized η-Ricci solitons on LP-Sasakian manifolds admitting the general connection (Murat Altunbaş and Ayşe Karanlık Akpınar, 2025)5Altunbaş 2025 K-contact manifolds admitting some geometric solitons with Semi-Symmetric Non-Metric Connection (Bidhan Mondal, Nirabhra Basu and Arindam Bhattacharyya, 2026)7Mondal 2026
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  1. 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 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, Ricci solitons · Same authors Santu Dey, Arindam Bhattacharyya · Shared terms “manifold admitting”

  3. 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

  4. Sasakian Manifold and *-Ricci Tensor

    Venkatesha. and Aruna Kumara H

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

  5. Generalized Ricci solitons on LP-Sasakian manifolds admitting the general connection

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    Topics Sasakian & contact geometry, Ricci solitons · Shared terms “manifold admitting”

  6. Remarks on almost -Ricci solitons in -para Sasakian manifolds

    Adara M. Blaga and Selcen Yuksel Perktas

    Topics Sasakian & contact geometry, Almost & η-Ricci solitons, Ricci solitons · Shared terms “manifolds satisfying”, “curvature tensor”

  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 · Same author Arindam Bhattacharyya · Shared terms “Pseudo projective”, “manifold admitting”

  8. Invariant and anti-invariant submanifolds of special quasi-sasakian manifolds

    Shyamal Kumar Hui and Joydeb Roy

    Topics Sasakian & contact geometry, Ricci solitons · Same author Shyamal Kumar Hui

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.