Paper · Jan 18, 2020

Almost Hermitian Ricci flow

Casey Lynn Kelleher, Gang Tian

math.DGarXiv:2001.06670v2
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Abstract

We introduce a new curvature flow which matches with the Ricci flow on metrics and preserves the almost Hermitian condition. This enables us to use Ricci flow to study almost Hermitian manifolds.

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Submitted
Jan 18, 2020
Last revised
Mar 26, 2020 (v2)
Subjects
math.DG
Ricci flowOther curvature flows

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 Singular limits of Kähler-Ricci flow on Fano G-manifolds (Yan Li, Gang Tian and Xiaohua Zhu, 2018)7Li 2018 Symplectic curvature flow revisited (Casey Lynn Kelleher, 2018)1Kelleher 2018 Quantum flag manifold σ-models and Hermitian Ricci flow (Dmitri Bykov, 2020)2Bykov 2020 Kähler stability of symplectic forms (Jeffrey Streets and Gang Tian, 2022)4Streets 2022 Finite time singularities of the Kähler-Ricci flow (Wangjian Jian, Jian Song and Gang Tian, 2023)6Jian 2023 Geometric regularity of blow-up limits of the Kähler-Ricci flow (Max Hallgren, Wangjian Jian, Jian Song et al., 2023)8Hallgren 2023 Some remarks on strong G₂-structures with torsion (Anna Fino and Udhav Fowdar, 2025)3Fino 2025 Almost Hermitian geometry and generalized Ricci flow (Anna Fino and Julieth Saavedra, 2026)5Fino 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Symplectic curvature flow revisited

    Casey Lynn Kelleher

    Topics Other curvature flows · Same author Casey Lynn Kelleher

  2. Quantum flag manifold -models and Hermitian Ricci flow

    Dmitri Bykov

    Topics Ricci flow · Shared terms “hermitian ricci”

  3. Some remarks on strong -structures with torsion

    Anna Fino and Udhav Fowdar

    Topics Ricci flow · Shared terms “almost Hermitian”

  4. Kähler stability of symplectic forms

    Jeffrey Streets and Gang TianWider flows

    Topics Other curvature flows · Same author Gang Tian

  5. Almost Hermitian geometry and generalized Ricci flow

    Anna Fino and Julieth Saavedra

    Topics Ricci flow · Shared terms “almost Hermitian”, “Hermitian manifolds”

  6. Finite time singularities of the Kähler-Ricci flow

    Wangjian Jian, Jian Song and Gang Tian

    Topics Ricci flow · Same author Gang Tian

  7. Singular limits of Kähler-Ricci flow on Fano -manifolds

    Yan Li, Gang Tian and Xiaohua Zhu

    Topics Ricci flow · Same author Gang Tian

  8. Geometric regularity of blow-up limits of the Kähler-Ricci flow

    Max Hallgren, Wangjian Jian, Jian Song et al.

    Topics Ricci flow · Same author Gang Tian

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) Other curvature flows Wider flows Flows that move a hypersurface or metric by some other function of curvature: Gauss curvature (worn stones), inverse mean curvature (the Penrose… Start with: Shapes of worn stones (Firey, 1974)

In the guidebook

  1. 5A.5
    Uniformization and the Two-Dimensional Ricci FlowBook 5A · Complex Analysis and Conformal Geometry

    Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.

  2. 10A.12
    Curve Shortening and Minimal DiscsBook 10A · Three-Manifolds and Geometrization

    How loops shrink under curvature, how the discs they bound lose area, and Perelman's extinction estimate.

  3. 11A.1
    The Equation and Its First SolutionsBook 11A · The Ricci Flow: Existence and Maximum Principles

    A heat equation for the metric: spheres, cylinders and scaling.