Paper · Jan 5, 2018

Para-Sasakian manifolds and *-Ricci solitons

D. G. Prakasha, Pundikala Veeresha

math.DGarXiv:1801.01727
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Abstract

In this paper we study a special type of metric called *-Ricci soliton on para-Sasakian manifold. We prove that if the para-Sasakian metric is a *-Ricci soliton on a manifold M, then M is either D-homothetic to an Einstein manifold, or the Ricci tensor of M with respect to the canonical paracontact connection vanishes.

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Submitted
Jan 5, 2018
Subjects
math.DG

Comments: 12 pages

Ricci solitonsEinstein metricsAlmost & 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 η-Ricci solitons in (ε)-almost paracontact metric manifolds (Adara Monica Blaga, Selcen Yüksel Perktaş, Bilal Eftal Acet et al., 2017)5Blaga 2017 Remarks on almost η-Ricci solitons in (ε)-para Sasakian manifolds (Adara M. Blaga and Selcen Yuksel Perktas, 2018)1Blaga 2018 Sasakian Manifold and *-Ricci Tensor (Venkatesha. and Aruna Kumara H, 2018)3Venkatesha. 2018 *-Conformal η-Ricci Soliton on Sasakian manifold (Soumendu Roy, Santu Dey, Arindam Bhattacharyya et al., 2019)4Roy 2019 Characteristics of almost conformal Ricci solitons on Sasakian manifold (Dipen Ganguly, Nirabhra Basu and Arindam Bhattacharyya, 2021)7Ganguly 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)6Altunbaş 2025 Complete gradient Einstein-type Sasakian manifolds with α=0 (Shun Maeta, 2025)8Maeta 2025
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. 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 “para Sasakian”

  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, Einstein metrics · Shared terms “para Sasakian”

  3. Sasakian Manifold and *-Ricci Tensor

    Venkatesha. and Aruna Kumara H

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

  4. *-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

  5. -Ricci solitons in -almost paracontact metric manifolds

    Adara Monica Blaga, Selcen Yüksel Perktaş, Bilal Eftal Acet et al.

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

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

    Murat Altunbaş and Ayşe Karanlık Akpınar

    Topics Sasakian & contact geometry, Ricci solitons

  7. 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

  8. Complete gradient Einstein-type Sasakian manifolds with

    Shun Maeta

    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) 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) 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.