Paper · Jul 12, 2017

Ricci solitons on Ricci pseudosymmetric -manifolds

Shyamal Kumar Hui, Richard S. Lemence, Debabrata Chakraborty

math.DGarXiv:1707.03618
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Abstract

The object of the present paper is to study some types of Ricci pseudosymmetric -manifolds whose metric is Ricci soliton. We found the conditions when Ricci soliton on concircular Ricci pseudosymmetric, projective Ricci pseudosymmetric, -Ricci pseudosymmetric, conharmonic Ricci pseudosymmetric, conformal Ricci pseudosymmetric -manifolds to be shrinking, steady and expanding. We also construct an example of concircular Ricci pseudosymmetric -manifold whose metric is Ricci soliton.

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Submitted
Jul 12, 2017
Subjects
math.DG

Comments: 21 pages

Ricci solitons

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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 Invariant submanifolds of generalized Sasakian-space-forms (Shyamal Kumar Hui, Siraj Uddin, Ali H. Alkhaldi et al., 2017)8Hui 2017 Ricci Solitons on submanifolds of (LCS)ₙ-Manifolds (Shyamal Kumar Hui, Rajendra Prasad and Tanumoy Pal, 2017)5Hui 2017 Invariant and anti-invariant submanifolds of special quasi-sasakian manifolds (Shyamal Kumar Hui and Joydeb Roy, 2017)7Hui 2017 Certain results on (LCS)n-manifolds (Vishnuvardhana. S. V., Venkatesha and S. K. Hui, 2019)3V. 2019 *-Conformal η-Ricci Soliton on Sasakian manifold (Soumendu Roy, Santu Dey, Arindam Bhattacharyya et al., 2019)4Roy 2019 A Study On Some Geometric Properties and Physical Applications of A Mixed Quasi-Einstein Spacetime (Kaushik Chattopadhyay, Arindam Bhattacharyya and Dipankar Debnath, 2021)6Chattopadhya 2021 On curvature related geometric properties of Hayward black hole spacetime (Absos Ali Shaikh, Shyamal Kumar Hui, Biswa Ranjan Datta et al., 2023)1Shaikh 2023 Symmetry and pseudosymmetry properties of Vaidya-Bonner-de Sitter spacetime (Absos Ali Shaikh, Shyamal kumar Hui, Mousumi Sarkar et al., 2024)2Shaikh 2024
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. On curvature related geometric properties of Hayward black hole spacetime

    Absos Ali Shaikh, Shyamal Kumar Hui, Biswa Ranjan Datta et al.

    Topics Ricci solitons · Same author Shyamal Kumar Hui · Shared terms “pseudosymmetric”, “concircular”, “conharmonic”

  2. Symmetry and pseudosymmetry properties of Vaidya-Bonner-de Sitter spacetime

    Absos Ali Shaikh, Shyamal kumar Hui, Mousumi Sarkar et al.

    Topics Ricci solitons · Same author Shyamal Kumar Hui · Shared terms “pseudosymmetric”, “conharmonic”

  3. Certain results on (LCS)n-manifolds

    Vishnuvardhana. S. V., Venkatesha and S. K. Hui

    Topics Ricci solitons · Same author Shyamal Kumar Hui · Shared terms “conformal Ricci”

  4. *-Conformal η-Ricci Soliton on Sasakian manifold

    Soumendu Roy, Santu Dey, Arindam Bhattacharyya et al.

    Topics Ricci solitons · Same author Shyamal Kumar Hui · Shared terms “projective”

  5. Ricci Solitons on submanifolds of -Manifolds

    Shyamal Kumar Hui, Rajendra Prasad and Tanumoy Pal

    Topics Ricci solitons · Same author Shyamal Kumar Hui

  6. A Study On Some Geometric Properties and Physical Applications of A Mixed Quasi-Einstein Spacetime

    Kaushik Chattopadhyay, Arindam Bhattacharyya and Dipankar Debnath

    Topics Ricci solitons · Shared terms “Ricci pseudosymmetric”, “projective Ricci”

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

    Shyamal Kumar Hui and Joydeb Roy

    Topics Ricci solitons · Same author Shyamal Kumar Hui

  8. Invariant submanifolds of generalized Sasakian-space-forms

    Shyamal Kumar Hui, Siraj Uddin, Ali H. Alkhaldi et al.

    Topics 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)

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.