Paper · May 11, 2017

Solitons and geometrical structures in a perfect fluid spacetime

Adara M. Blaga

math.DGarXiv:1705.04094v4
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Abstract

Geometrical aspects of a perfect fluid spacetime are described in terms of different curvature tensors and -Ricci and -Einstein solitons in a perfect fluid spacetime are determined. Conditions for the Ricci soliton to be steady, expanding or shrinking are also given. In a particular case when the potential vector field of the soliton is of gradient type, , we derive a Poisson equation from the soliton equation.

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Submitted
May 11, 2017
Last revised
Aug 23, 2020 (v4)
Subjects
math.DG
Journal
Rocky Mountain Journal of Mathematics 50(1), 41-53 (2020)
DOI
10.1216/rmj.2020.50.41

Comments: 19 pages

Ricci solitonsAlmost & η-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 On warped product gradient η-Ricci solitons (Adara M. Blaga, 2017)7Blaga 2017 Harmonic aspects in an η-Ricci soliton (Adara M. Blaga, 2018)2Blaga 2018 Ricci Soliton and Geometrical Structure in a Perfect Fluid Spacetime with Torse-forming Vector Field (Venkatesha and Aruna Kumara H, 2018)4Venkatesha 2018 Remarks on almost Riemann solitons with gradient or torse-forming vector field (Adara M. Blaga, 2020)8Blaga 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)1Suh 2022 On some 3-dimensional almost η-Ricci solitons with diagonal metrics (Adara M. Blaga, 2024)6Blaga 2024 Almost Gradient Ricci Solitons on Static Spacetime (Akhilesh Yadav and Tarun Saxena, 2025)5Yadav 2025
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Characterizations of Perfect fluid spacetimes obeying -gravity equipped with different gradient solitons

    Krishnendu De Young Jin Suh and Uday Chand De

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “fluid spacetime”, “perfect fluid”, “Einstein soliton”

  2. Harmonic aspects in an -Ricci soliton

    Adara M. Blaga

    Topics Almost & η-Ricci solitons, Ricci solitons · Same author Adara M. Blaga · Shared terms “fluid spacetime”, “perfect fluid”

  3. Perfect fluid spacetimes and gradient solitons

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

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “fluid spacetime”, “perfect fluid”, “Einstein soliton”

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

    Venkatesha and Aruna Kumara H

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

  5. Almost Gradient Ricci Solitons on Static Spacetime

    Akhilesh Yadav and Tarun Saxena

    Topics Almost & η-Ricci solitons, Ricci solitons · Shared terms “fluid spacetime”, “perfect fluid”, “geometrical aspects”

  6. On some -dimensional almost -Ricci solitons with diagonal metrics

    Adara M. Blaga

    Topics Almost & η-Ricci solitons, Ricci solitons · Same author Adara M. Blaga · Shared terms “potential vector”, “vector field”

  7. On warped product gradient -Ricci solitons

    Adara M. Blaga

    Topics Almost & η-Ricci solitons, Ricci solitons · Same author Adara M. Blaga · Shared terms “potential vector”, “gradient type”, “vector field”

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

    Adara M. Blaga

    Topics Almost & η-Ricci solitons, Ricci solitons · Same author Adara M. Blaga · Shared terms “gradient type”, “vector field”, “potential vector”

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)

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.