Paper · May 14, 2017

Randers Ricci soliton homogeneous nilmanifolds

Hamid Reza Salimi Moghaddam

math.DGarXiv:1705.04957v2
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Abstract

Let be a left invariant Randers metric on a simply connected nilpotent Lie group , induced by a left invariant Riemannian metric and a vector field which is -invariant. If the Ricci flow equation has a unique solution then, is a Ricci soliton if and only if is a semialgebraic Ricci soliton.

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Submitted
May 14, 2017
Last revised
Dec 9, 2019 (v2)
Subjects
math.DG
Journal
MATHEMATICA SCANDINAVICA. 127, 1 (Feb. 2021), 100-110
DOI
10.7146/math.scand.a-122610
Ricci flowRicci solitonsHomogeneous spaces

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 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 On the classification of five-dimensional nilsolitons (Hamid Reza Salimi Moghaddam, 2019)4Moghaddam 2019 Generalized Ricci flow on nilpotent Lie groups (Fabio Paradiso, 2020)8Paradiso 2020 A classification of left-invariant Lorentzian metrics on some nilpotent Lie groups (Yuji Kondo and Hiroshi Tamaru, 2020)7Kondo 2020 Classification of Left Invariant Riemannian metrics on Complex hyperbolic space (Andrijana Dekic, Marijana Babic and Srdjan Vukmirovic, 2021)6Dekic 2021 Lorentz Ricci solitons of 4-dimensional non-Abelian nilpotent Lie groups (Rohollah Bakhshandeh-Chamazkoti, 2021)5Bakhshandeh- 2021 Nilpotent Lie algebras obtained by quivers and Ricci solitons (Fumika Mizoguchi and Hiroshi Tamaru, 2024)2Mizoguchi 2024 Ricci Solitons of Left-Invariant Metrics on Lie Groups with Derived Algebra of Dimension at Most Two (Hamid Reza Salimi Moghaddam, 2026)1Moghaddam 2026 Sectional Curvature Pinching of Two-Step Nilmanifolds (Tomoya Tatsuno, 2026)3Tatsuno 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 Left-Invariant Metrics on Lie Groups with Derived Algebra of Dimension at Most Two

    Hamid Reza Salimi Moghaddam

    Topics Homogeneous spaces, Ricci solitons · Same author Hamid Reza Salimi Moghaddam · Shared terms “left invariant”, “invariant Riemannian”, “Lie groups”

  2. Nilpotent Lie algebras obtained by quivers and Ricci solitons

    Fumika Mizoguchi and Hiroshi Tamaru

    Topics Homogeneous spaces, Ricci solitons · Shared terms “nilpotent Lie”, “left invariant”, “nilmanifolds”

  3. Sectional Curvature Pinching of Two-Step Nilmanifolds

    Tomoya Tatsuno

    Topics Homogeneous spaces, Ricci solitons · Shared terms “nilmanifolds”, “nilpotent Lie”, “left invariant”

  4. On the classification of five-dimensional nilsolitons

    Hamid Reza Salimi Moghaddam

    Topics Homogeneous spaces, Ricci solitons · Same author Hamid Reza Salimi Moghaddam · Shared terms “nilmanifolds”

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

    Rohollah Bakhshandeh-Chamazkoti

    Topics Homogeneous spaces, Ricci solitons · Shared terms “left invariant”, “nilpotent Lie”, “Lie groups”

  6. Classification of Left Invariant Riemannian metrics on Complex hyperbolic space

    Andrijana Dekic, Marijana Babic and Srdjan Vukmirovic

    Topics Homogeneous spaces, Ricci solitons · Shared terms “left invariant”, “invariant Riemannian”, “Lie groups”

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

    Yuji Kondo and Hiroshi Tamaru

    Topics Homogeneous spaces, Ricci solitons · Shared terms “left invariant”, “nilpotent Lie”, “Lie groups”

  8. Generalized Ricci flow on nilpotent Lie groups

    Fabio Paradiso

    Topics Homogeneous spaces · Shared terms “nilpotent Lie”, “connected nilpotent”, “Lie groups”

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 flow Hamilton's Ricci flow evolves a Riemannian metric by minus twice its Ricci curvature. It is a nonlinear heat equation for geometry: it spreads… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982) 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) 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. 11A.13
    Homogeneous FlowsBook 11A · The Ricci Flow: Existence and Maximum Principles

    A computable laboratory: the flow on Thurston’s geometries.

  2. 11B.1
    Ricci SolitonsBook 11B · Solitons, Compactness and Singularities

    Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.

  3. 12B.2
    The Asymptotic Soliton and Three-Dimensional ShrinkersBook 12B · κ-Solutions and Surgery

    Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.