Paper · Jul 27, 2018

Sasakian Manifold and *-Ricci Tensor

Venkatesha., Aruna Kumara H

math.DGarXiv:1807.10541
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Abstract

The purpose of this paper is to study *-Ricci tensor on Sasakian manifold. Here, φ-confomally flat and confomally flat *-η-Einstein Sasakian manifold are studied. Next, we consider *-Ricci symmetric conditon on Sasakian manifold. Finally, we study a special type of metric called *-Ricci soliton on Sasakian manifold.

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Submitted
Jul 27, 2018
Subjects
math.DG
Ricci solitonsAlmost & η-Ricci solitonsSasakian & contact geometry

Its neighbourhood

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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 Para-Sasakian manifolds and *-Ricci solitons (D. G. Prakasha and Pundikala Veeresha, 2018)2Prakasha 2018 Remarks on almost η-Ricci solitons in (ε)-para Sasakian manifolds (Adara M. Blaga and Selcen Yuksel Perktas, 2018)6Blaga 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 Ricci solitons and certain related metrics on 3-dimensional trans-Sasakian manifold (Sumanjit Sarkar, Santu Dey and Arindam Bhattacharyya, 2021)8Sarkar 2021 Sasakian lift of Kaehler manifold and α-Sasakian Ricci solitons (Piotr Dacko, 2023)7Dacko 2023 Generalized η-Ricci solitons on LP-Sasakian manifolds admitting the general connection (Murat Altunbaş and Ayşe Karanlık Akpınar, 2025)3Altunbaş 2025 Complete gradient Einstein-type Sasakian manifolds with α=0 (Shun Maeta, 2025)4Maeta 2025
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

  2. Para-Sasakian manifolds and *-Ricci solitons

    D. G. Prakasha and Pundikala Veeresha

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

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

    Murat Altunbaş and Ayşe Karanlık Akpınar

    Topics Sasakian & contact geometry, Ricci solitons

  4. Complete gradient Einstein-type Sasakian manifolds with

    Shun Maeta

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

  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

  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

  7. Sasakian lift of Kaehler manifold and -Sasakian Ricci solitons

    Piotr Dacko

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

  8. 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

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.