Paper · Mar 25, 2019

Hermitian Curvature Flow on compact homogeneous spaces

Francesco Panelli, Fabio Podestà

math.DGarXiv:1903.10273
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Abstract

We study a version of the Hermitian curvature flow on compact homogeneous complex manifolds. We prove that the solution has a finite exstinction time and we analyze its behaviour when . We also determine the invariant static metrics and we study the convergence of the normalized flow to one of them.

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Submitted
Mar 25, 2019
Subjects
math.DG
Generalized & G₂ flowsHomogeneous 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 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 Hermitian Curvature flow on unimodular Lie groups and static invariant metrics (Ramiro A. Lafuente, Mattia Pujia and Luigi Vezzoni, 2018)4Lafuente 2018 Expanding solitons to the Hermitian curvature flow on complex Lie groups (Mattia Pujia, 2018)5Pujia 2018 Hermitian curvature flow on complex locally homogeneous surfaces (Francesco Pediconi and Mattia Pujia, 2019)2Pediconi 2019 Positive Hermitian curvature flow on complex 2-step nilpotent Lie groups (Mattia Pujia, 2020)6Pujia 2020 Collapsed ancient solutions of the Ricci flow on compact homogeneous spaces (Francesco Pediconi and Sammy Sbiti, 2021)8Pediconi 2021 Positive Hermitian Curvature Flow on special linear groups and perfect solitons (James Stanfield, 2021)3Stanfield 2021 Bismut Ricci flat manifolds with symmetries (Fabio Podestà and Alberto Raffero, 2022)1Podestà 2022 Positive Hermitian curvature flow on 2-step nilpotent Lie groups (Ettore Lo Giudice, 2025)7Giudice 2025
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Bismut Ricci flat manifolds with symmetries

    Fabio Podestà and Alberto Raffero

    Topics Generalized & G₂ flows, Homogeneous spaces · Same author Fabio Podestà · Shared terms “compact homogeneous”

  2. Hermitian curvature flow on complex locally homogeneous surfaces

    Francesco Pediconi and Mattia Pujia

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

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

    James Stanfield

    Topics Generalized & G₂ flows, Homogeneous spaces · Shared terms “Hermitian curvature”, “static metrics”

  4. Hermitian Curvature flow on unimodular Lie groups and static invariant metrics

    Ramiro A. Lafuente, Mattia Pujia and Luigi Vezzoni

    Topics Generalized & G₂ flows, Homogeneous spaces · Shared terms “Hermitian curvature”, “static metrics”

  5. Expanding solitons to the Hermitian curvature flow on complex Lie groups

    Mattia Pujia

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

  6. Positive Hermitian curvature flow on complex 2-step nilpotent Lie groups

    Mattia Pujia

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

  7. Positive Hermitian curvature flow on 2-step nilpotent Lie groups

    Ettore Lo Giudice

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

  8. Collapsed ancient solutions of the Ricci flow on compact homogeneous spaces

    Francesco Pediconi and Sammy Sbiti

    Topics Homogeneous spaces · Shared terms “compact homogeneous”

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) 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.