Paper · Nov 10, 2025

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

Giovanni Calvaruso, Lorenzo Pellegrino, Amirhesam Zaeim

math.DGarXiv:2511.06923
View PDF View HTML arXiv page

As on arXiv

Abstract

In the framework of the study of homogeneous Lorentzian three-manifolds, we consider here the only class of examples which admit a four-dimensional group of isometries but are neither Lorentzian Bianchi-Cartan-Vranceanu spaces nor plane waves. We obtain an explicit description in global coordinates of these special homogeneous Lorentzian manifolds. We then prove that all such examples are non-gradient expanding Ricci solitons.

View PDF View HTML arXiv page
Submitted
Nov 10, 2025
Subjects
math.DG

Comments: 12 pages. Accepted for publication in the Journal of Lie Theory

Ricci solitons3-manifolds4-manifoldsHomogeneous spacesPhysics

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 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 Lorentz Ricci solitons of 4-dimensional non-Abelian nilpotent Lie groups (Rohollah Bakhshandeh-Chamazkoti, 2021)5Bakhshandeh- 2021 Pseudo-Riemannian Algebraic Ricci Solitons on Four-Dimensional Lie Groups (Youssef Ayad, 2026)6Ayad 2026 Four-dimensional Lorentzian algebraic Ricci solitons (Eduardo Garcia-Rio, Rosalia Rodriguez-Gigirey and Ramon Vazquez-Lorenzo, 2026)2Garcia-Rio 2026 Canonical Connections and Algebraic Ricci Solitons on Lorentzian 4-Dimensional Nilpotent Lie Groups (Youssef Ayad, 2026)3Ayad 2026 Lorentzian Algebraic Ricci Solitons on the Heisenberg Group (Youssef Ayad, 2026)8Ayad 2026 Algebraic and Symmetrized Affine star-Ricci Solitons for the Bott Connection on Three-Dimensional Lorentzian Lie Groups (Yuxin Ding, 2026)7Ding 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)4Lin 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 “Bianchi Cartan”, “Cartan Vranceanu”, “Lorentzian Bianchi”

  2. Four-dimensional Lorentzian algebraic Ricci solitons

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

    Topics 4-manifolds, Physics, Homogeneous spaces · Shared terms “Lorentzian”, “four dimensional”, “Lie groups”

  3. Canonical Connections and Algebraic Ricci Solitons on Lorentzian 4-Dimensional Nilpotent Lie Groups

    Youssef Ayad

    Topics 4-manifolds, Physics, Homogeneous spaces · Shared terms “Lorentzian”, “Lie groups”, “four dimensional”

  4. 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, Homogeneous spaces · Shared terms “Lorentzian Lie”, “Lie groups”, “isometry”

  5. Lorentz Ricci solitons of 4-dimensional non-Abelian nilpotent Lie groups

    Rohollah Bakhshandeh-Chamazkoti

    Topics 4-manifolds, Physics, Homogeneous spaces · Shared terms “Lie groups”, “Lorentzian”

  6. Pseudo-Riemannian Algebraic Ricci Solitons on Four-Dimensional Lie Groups

    Youssef Ayad

    Topics 4-manifolds, Homogeneous spaces, Ricci solitons · Shared terms “four dimensional”, “Lie groups”, “description”

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

    Yuxin Ding

    Topics Physics, 3-manifolds, Homogeneous spaces · Shared terms “Lorentzian Lie”, “Lie groups”

  8. Lorentzian Algebraic Ricci Solitons on the Heisenberg Group

    Youssef Ayad

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

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) 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) 4-manifolds Four is the first dimension where Ricci flow's singularities are not fully understood. It is also the dimension of the smooth Poincaré conjecture… Start with: The topology of four-dimensional manifolds (Freedman, 1982) Homogeneous spaces On homogeneous spaces Ricci flow reduces to an ordinary differential equation on a finite-dimensional space of invariant metrics. Start with: Ricci flow of locally homogeneous geometries on closed manifolds (Isenberg et al., 1992)

In the guidebook

  1. 10A.1
    A Zoo of Three-ManifoldsBook 10A · Three-Manifolds and Geometrization

    The 3-sphere, lens spaces, the Poincaré sphere, the Hopf fibration and the shape of space.

  2. 10A.2
    Finite Rotation Groups and Spherical Space FormsBook 10A · Three-Manifolds and Geometrization

    Klein's classification by counting poles, the binary groups, and every quotient of the round 3-sphere.

  3. 10A.4
    Homotopy Groups, Degree and the Hurewicz TheoremBook 10A · Three-Manifolds and Geometrization

    Spheres mapped into manifolds: the algebraic topology that finite extinction runs on.