Paper · Dec 21, 2020

Affine Ricci solitons of three-dimensional Lorentzian Lie groups

Yong Wang

math.DGarXiv:2012.11421
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Abstract

In this paper, we classify affine Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections and perturbed canonical connections and perturbed Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups with some product structure.

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Submitted
Dec 21, 2020
Subjects
math.DG

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Ricci solitons3-manifoldsHomogeneous spacesPhysics

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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 Lorentzian left invariant metrics on three dimensional unimodular Lie groups and their curvatures (Mohamed Boucetta and Abdelmounaim Chakkar, 2019)8Boucetta 2019 Canonical connections and algebraic Ricci solitons of three-dimensional Lorentzian Lie groups (Yong Wang, 2020)1Wang 2020 A classification of left-invariant Lorentzian metrics on some nilpotent Lie groups (Yuji Kondo and Hiroshi Tamaru, 2020)7Kondo 2020 Affine Ricci Solitons associated to the Bott connection on three-dimensional Lorentzian Lie groups (Tong Wu and Yong Wang, 2021)2Wu 2021 Ricci solitons of special Lorentzian Lie groups with a four-dimensional isometry group (Giovanni Calvaruso, Lorenzo Pellegrino and Amirhesam Zaeim, 2025)6Calvaruso 2025 Canonical Connections and Algebraic Ricci Solitons on Lorentzian 4-Dimensional Nilpotent Lie Groups (Youssef Ayad, 2026)4Ayad 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)3Lin 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Canonical connections and algebraic Ricci solitons of three-dimensional Lorentzian Lie groups

    Yong Wang

    Topics Physics, 3-manifolds, Homogeneous spaces · Same author Yong Wang · Shared terms “Lorentzian Lie”, “dimensional Lorentzian”, “canonical connections”

  2. Affine Ricci Solitons associated to the Bott connection on three-dimensional Lorentzian Lie groups

    Tong Wu and Yong Wang

    Topics Physics, 3-manifolds, Homogeneous spaces · Same author Yong Wang · Shared terms “affine Ricci”, “Lorentzian Lie”, “dimensional Lorentzian”

  3. 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 “affine Ricci”, “Lorentzian Lie”, “dimensional Lorentzian”

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

    Youssef Ayad

    Topics Physics, Homogeneous spaces, Ricci solitons · Shared terms “canonical connections”, “Kobayashi Nomizu”, “Nomizu connections”

  5. 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”, “dimensional Lorentzian”, “Lie groups”

  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, Homogeneous spaces · Shared terms “Lorentzian Lie”, “Lie groups”

  7. A classification of left-invariant Lorentzian metrics on some nilpotent Lie groups

    Yuji Kondo and Hiroshi Tamaru

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

  8. Lorentzian left invariant metrics on three dimensional unimodular Lie groups and their curvatures

    Mohamed Boucetta and Abdelmounaim Chakkar

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

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) 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) 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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