Paper · May 17, 2021

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

Tong Wu, Yong Wang

math.DGarXiv:2105.07557
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As on arXiv

Abstract

In this paper, we compute the Bott connections and their curvature on three-dimensional Lorentzian Lie groups with three different distributions, and we classify affine Ricci solitons associated to the Bott connection on three-dimensional Lorentzian Lie groups with three different distributions.

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Submitted
May 17, 2021
Subjects
math.DG
Ricci solitons3-manifoldsHomogeneous spacesPhysics

Its neighbourhood

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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)2Wang 2020 A classification of left-invariant Lorentzian metrics on some nilpotent Lie groups (Yuji Kondo and Hiroshi Tamaru, 2020)6Kondo 2020 Affine Ricci solitons of three-dimensional Lorentzian Lie groups (Yong Wang, 2020)1Wang 2020 Ricci solitons of special Lorentzian Lie groups with a four-dimensional isometry group (Giovanni Calvaruso, Lorenzo Pellegrino and Amirhesam Zaeim, 2025)5Calvaruso 2025 Canonical Connections and Algebraic Ricci Solitons on Lorentzian 4-Dimensional Nilpotent Lie Groups (Youssef Ayad, 2026)7Ayad 2026 Algebraic and Symmetrized Affine star-Ricci Solitons for the Bott Connection on Three-Dimensional Lorentzian Lie Groups (Yuxin Ding, 2026)4Ding 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
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  1. Affine Ricci solitons of three-dimensional Lorentzian Lie groups

    Yong Wang

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

  2. 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”, “solitons associated”

  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. 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 “Bott connection”, “Lorentzian Lie”, “dimensional Lorentzian”

  5. 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”

  6. 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”

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

    Youssef Ayad

    Topics Physics, Homogeneous spaces, Ricci solitons · Shared terms “solitons associated”, “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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