Paper · Jun 2, 2018

Ricci Soliton and Geometrical Structure in a Perfect Fluid Spacetime with Torse-forming Vector Field

Venkatesha, Aruna Kumara H

math.DGarXiv:1806.00599
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Abstract

In this paper geometrical aspects of perfect fluid spacetime with torse-forming vector field ξare discribed and Ricci soliton in perfect fluid spacetime with torse-forming vector field ξare determined. Conditions for the Ricci soliton to be expanding, steady or shrinking are also given.

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Submitted
Jun 2, 2018
Subjects
math.DG
Ricci solitons

Its neighbourhood

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 Solitons and geometrical structures in a perfect fluid spacetime (Adara M. Blaga, 2017)1Blaga 2017 Kinematic Description of Ricci Solitons in Fluid Spacetimes (Umber Sheikh, 2017)4Sheikh 2017 Harmonic aspects in an η-Ricci soliton (Adara M. Blaga, 2018)8Blaga 2018 Remarks on almost Riemann solitons with gradient or torse-forming vector field (Adara M. Blaga, 2020)2Blaga 2020 Perfect fluid spacetimes and gradient solitons (Krishnendu De Uday Chand De, Abdallah Abdelhameed Syied, Nasser Bin Turki et al., 2021)3De 2021 Characterizations of Perfect fluid spacetimes obeying f(𝓡)-gravity equipped with different gradient solitons (Krishnendu De Young Jin Suh and Uday Chand De, 2022)6Suh 2022 Characterizations of a Lorentzian Manifold with a semi-symmetric metric connection (Uday Chand De, Krishnendu De and Sinem Güler, 2024)5De 2024 Almost Gradient Ricci Solitons on Static Spacetime (Akhilesh Yadav and Tarun Saxena, 2025)7Yadav 2025
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Solitons and geometrical structures in a perfect fluid spacetime

    Adara M. Blaga

    Topics Ricci solitons · Shared terms “fluid spacetime”, “geometrical structure”, “perfect fluid”

  2. Remarks on almost Riemann solitons with gradient or torse-forming vector field

    Adara M. Blaga

    Topics Ricci solitons · Shared terms “torse forming”, “forming vector”, “vector field”

  3. Perfect fluid spacetimes and gradient solitons

    Krishnendu De Uday Chand De, Abdallah Abdelhameed Syied, Nasser Bin Turki et al.

    Topics Ricci solitons · Shared terms “fluid spacetime”, “perfect fluid”, “vector field”

  4. Kinematic Description of Ricci Solitons in Fluid Spacetimes

    Umber Sheikh

    Topics Ricci solitons · Shared terms “fluid spacetime”, “perfect fluid”

  5. Characterizations of a Lorentzian Manifold with a semi-symmetric metric connection

    Uday Chand De, Krishnendu De and Sinem Güler

    Topics Ricci solitons · Shared terms “fluid spacetime”, “perfect fluid”, “forming vector”

  6. Characterizations of Perfect fluid spacetimes obeying -gravity equipped with different gradient solitons

    Krishnendu De Young Jin Suh and Uday Chand De

    Topics Ricci solitons · Shared terms “fluid spacetime”, “perfect fluid”, “vector field”

  7. Almost Gradient Ricci Solitons on Static Spacetime

    Akhilesh Yadav and Tarun Saxena

    Topics Ricci solitons · Shared terms “fluid spacetime”, “perfect fluid”, “geometrical aspects”

  8. Harmonic aspects in an -Ricci soliton

    Adara M. Blaga

    Topics Ricci solitons · Shared terms “fluid spacetime”, “perfect fluid”

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.