Paper · Jul 13, 2021

Ricci solitons of three-dimensional Lorentzian Bianchi-Cartan-Vranceanu spaces

Murat Altunbaş

math.DGarXiv:2107.06117v3
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As on arXiv

Abstract

Explicit formulae for homogenous Ricci solitons on three-dimensional Lorentzian Bianchi-Cartan-Vranceanu spaces are obtained.

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Submitted
Jul 13, 2021
Last revised
May 18, 2022 (v3)
Subjects
math.DG
Ricci solitons3-manifoldsPhysics

Its neighbourhood

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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 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 “Bianchi Cartan”, “Cartan Vranceanu”, “Lorentzian Bianchi”

  2. Ricci Solitons on a family of three dimensional Lorentzian Walker manifolds

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

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

  3. Lorentzian Algebraic Ricci Solitons on the Heisenberg Group

    Youssef Ayad

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

  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, Ricci solitons · Shared terms “dimensional Lorentzian”

  5. Four-dimensional Lorentzian algebraic Ricci solitons

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

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

  6. Brownian Motion in the Hilbert Space of Quantum States along with the Ricci Flow and Stochastically Emergent Einstein-Hilbert Action: Formulating a Well-Defined Feynman Path-Integral Measure for Quantum Fields in the Presence of Gravity

    A. A. Varshovi

    Topics Physics, 3-manifolds

  7. 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”

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

    M. J. Luo

    Topics Physics, 3-manifolds · Shared terms “dimensional 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) 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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    Homotopy Groups, Degree and the Hurewicz TheoremBook 10A · Three-Manifolds and Geometrization

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