Paper · Aug 13, 2025

Ricci Solitons on a family of three dimensional Lorentzian Walker manifolds

A. Diatta, M. Ciss, A. S. Diallo

math.DGarXiv:2508.10217
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Abstract

A Ricci soliton is a natural generalization of an Einstein metric. On a pseudo-Riemannian manifold (M, g), it is defined by : $LX g + \rho = λ g, where X is a smooth vector field on M , LX denotes the Lie derivative in the direction of X, \rho is the Ricci tensor, and λ is a real constant. In this paper, we establish the existence of non-trivial Ricci solitons on a family of three-dimensional Lorentzian Walker manifolds.

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Submitted
Aug 13, 2025
Subjects
math.DG
Ricci solitonsEinstein metrics3-manifoldsPhysics

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 2021, 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 Ricci solitons of three-dimensional Lorentzian Bianchi-Cartan-Vranceanu spaces (Murat Altunbaş, 2021)1Altunbaş 2021 Characterizations of a Lorentzian Manifold with a semi-symmetric metric connection (Uday Chand De, Krishnendu De and Sinem Güler, 2024)7De 2024 Well-posedness of Ricci Flow in Lorentzian Spacetime and its Entropy Formula (M. J. Luo, 2025)8Luo 2025 Ricci solitons of special Lorentzian Lie groups with a four-dimensional isometry group (Giovanni Calvaruso, Lorenzo Pellegrino and Amirhesam Zaeim, 2025)6Calvaruso 2025 Four-dimensional Lorentzian algebraic Ricci solitons (Eduardo Garcia-Rio, Rosalia Rodriguez-Gigirey and Ramon Vazquez-Lorenzo, 2026)4Garcia-Rio 2026 Lorentzian Algebraic Ricci Solitons on the Heisenberg Group (Youssef Ayad, 2026)3Ayad 2026 Algebraic and Symmetrized Affine star-Ricci Solitons for the Bott Connection on Three-Dimensional Lorentzian Lie Groups (Yuxin Ding, 2026)5Ding 2026 A complete parameter classification of left-invariant Bott affine Ricci solitons for two rotated distributions on three-dimensional Lorentzian Lie groups (Fanqi Lin, 2026)2Lin 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Ricci solitons of three-dimensional Lorentzian Bianchi-Cartan-Vranceanu spaces

    Murat Altunbaş

    Topics Physics, 3-manifolds, Ricci solitons · Shared terms “dimensional Lorentzian”

  2. A complete parameter classification of left-invariant Bott affine Ricci solitons for two rotated distributions on three-dimensional Lorentzian Lie groups

    Fanqi Lin

    Topics Physics, 3-manifolds, Ricci solitons · Shared terms “dimensional Lorentzian”, “Lie”, “Ricci tensor”

  3. Lorentzian Algebraic Ricci Solitons on the Heisenberg Group

    Youssef Ayad

    Topics Physics, 3-manifolds, Ricci solitons · Shared terms “Lorentzian”, “Lie”

  4. Four-dimensional Lorentzian algebraic Ricci solitons

    Eduardo Garcia-Rio, Rosalia Rodriguez-Gigirey and Ramon Vazquez-Lorenzo

    Topics Physics, Ricci solitons · Shared terms “dimensional Lorentzian”, “Lie”

  5. Algebraic and Symmetrized Affine star-Ricci Solitons for the Bott Connection on Three-Dimensional Lorentzian Lie Groups

    Yuxin Ding

    Topics Physics, 3-manifolds, Ricci solitons · Shared terms “dimensional Lorentzian”, “Lie”, “vector field”

  6. Ricci solitons of special Lorentzian Lie groups with a four-dimensional isometry group

    Giovanni Calvaruso, Lorenzo Pellegrino and Amirhesam Zaeim

    Topics Physics, 3-manifolds, Ricci solitons · Shared terms “Lorentzian”, “Lie”

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

    Uday Chand De, Krishnendu De and Sinem Güler

    Topics Physics, Ricci solitons · Shared terms “Lorentzian”, “Walker”, “vector field”

  8. Well-posedness of Ricci Flow in Lorentzian Spacetime and its Entropy Formula

    M. J. Luo

    Topics Physics, 3-manifolds · Shared terms “dimensional Lorentzian”, “Riemannian manifolds”

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) 3-manifolds Dimension three is where Ricci flow has done its most complete work. It proves geometrization, describes the flow's long-time behaviour, and now… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982) Physics Ricci flow first appeared in physics, as the leading-order renormalization-group flow of the string sigma model (Friedan, 1980). Start with: Nonlinear Models in 2+ε Dimensions (Friedan, 1980)

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