Paper · Oct 5, 2026

Harmonic torsion of algebraic generalized Ricci solitons and the structure of solvable extensions

Huibin Chen, Zhiqi Chen, Fuhai Zhu

math.DGarXiv:2610.08859
PDF Abstract page

As on arXiv

Abstract

We prove harmonicity for nonshrinking algebraic generalized Ricci solitons and for all algebraic generalized Ricci solitons on solvable Lie algebras. In the solvable setting, we characterize expanding solitons by normal extensions of generalized nilsolitons, and derive a sharp rank bound.

Generalized & G₂ flowsRicci solitonsHomogeneous spaces

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 Positive Hermitian Curvature Flow on special linear groups and perfect solitons (James Stanfield, 2021)8Stanfield 2021 Generalized Ricci flow on aligned homogeneous spaces (Valeria Gutiérrez, 2024)6Gutiérrez 2024 Three-dimensional positively curved generalized Ricci solitons with SO(3)-symmetries (Fabio Podestà and Alberto Raffero, 2024)5Podestà 2024 The homogeneous generalized Ricci flow (Elia Fusi, Ramiro A. Lafuente and James Stanfield, 2024)4Fusi 2024 Homogeneous Generalized Ricci flows II (Elia Fusi, Ramiro A. Lafuente and James Stanfield, 2026)7Fusi 2026 Harmonicity and Existence of Algebraic Generalized Ricci Solitons (Huibin Chen, Zhiqi Chen and Fuhai Zhu, 2026)1Chen 2026 Solvable Algebraic Generalized Ricci Solitons in low dimensions (Lorenzo Mucciante, 2026)2Mucciante 2026 Generalized scalar curvature and Ricci flow on compact Lie groups (Zhiqi Chen, Jianhua Yu, Huibin Chen et al., 2026)3Chen 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Harmonicity and Existence of Algebraic Generalized Ricci Solitons

    Huibin Chen, Zhiqi Chen and Fuhai Zhu PDF

    Topics Generalized & G₂ flows, Homogeneous spaces, Ricci solitons · Same authors Huibin Chen, Zhiqi Chen, Fuhai Zhu · Shared terms “algebraic generalized”, “harmonic torsion”, “generalized nilsolitons”

  2. Solvable Algebraic Generalized Ricci Solitons in low dimensions

    Lorenzo Mucciante PDF

    Topics Generalized & G₂ flows, Homogeneous spaces, Ricci solitons · Shared terms “algebraic generalized”, “solvable”, “Lie algebras”

  3. Generalized scalar curvature and Ricci flow on compact Lie groups

    Zhiqi Chen, Jianhua Yu, Huibin Chen et al. PDF

    Topics Generalized & G₂ flows, Homogeneous spaces · Same authors Huibin Chen, Zhiqi Chen · Shared terms “Lie algebras”

  4. The homogeneous generalized Ricci flow

    Elia Fusi, Ramiro A. Lafuente and James Stanfield PDF

    Topics Generalized & G₂ flows, Homogeneous spaces, Ricci solitons · Shared terms “harmonic torsion”, “Lie”

  5. Three-dimensional positively curved generalized Ricci solitons with SO(3)-symmetries

    Fabio Podestà and Alberto Raffero PDF

    Topics Generalized & G₂ flows, Homogeneous spaces, Ricci solitons

  6. Generalized Ricci flow on aligned homogeneous spaces

    Valeria Gutiérrez PDF

    Topics Generalized & G₂ flows, Homogeneous spaces · Shared terms “Lie”

  7. Homogeneous Generalized Ricci flows II

    Elia Fusi, Ramiro A. Lafuente and James Stanfield PDF

    Topics Generalized & G₂ flows, Homogeneous spaces, Ricci solitons · Shared terms “Lie algebras”

  8. Positive Hermitian Curvature Flow on special linear groups and perfect solitons

    James Stanfield PDF

    Topics Generalized & G₂ flows, Homogeneous spaces · Shared terms “algebraic”, “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.

Generalized & G₂ flows Ricci-type flows for geometry beyond Kähler metrics. Generalized Ricci flow couples a metric to a closed 3-form, pluriclosed and Chern–Ricci flows… Start with: A parabolic flow of pluriclosed metrics (Streets et al., 2009) 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.