Paper · Jun 4, 2019

Geometric formalities along the Chern-Ricci flow

Daniele Angella, Tommaso Sferruzza

math.DGarXiv:1906.01424v2
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Abstract

In this paper, we study how the notions of geometric formality according to Kotschick and other geometric formalities adapted to the Hermitian setting evolve under the action of the Chern-Ricci flow on class VII surfaces, including Hopf and Inoue surfaces, and on Kodaira surfaces.

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Submitted
Jun 4, 2019
Last revised
Dec 23, 2019 (v2)
Subjects
math.DG, math.CV
Journal
Complex Anal. Oper. Theory 2020 (2020), no. 2, 14-27
DOI
10.1007/s11785-019-00971-6

Comments: to appear in Complex Anal. Oper. Theory

Ricci flowGeneralized & G₂ 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 Weak Solutions of the Chern-Ricci flow on compact complex surfaces (Xiaolan Nie, 2017)5Nie 2017 On Gauduchon connections with Kähler-like curvature (Daniele Angella, Antonio Otal, Luis Ugarte et al., 2018)7Angella 2018 The Chern-Ricci flow on primary Hopf surfaces (Gregory Edwards, 2019)6Edwards 2019 Leafwise flat forms on Inoue-Bombieri surfaces (Daniele Angella and Valentino Tosatti, 2021)2Angella 2021 The Chern-Ricci flow (Valentino Tosatti and Ben Weinkove, 2021)1Tosatti 2021 Hermitian metrics on complex non-Kähler manifolds (Daniele Angella, 2025)4Angella 2025 On the Calabi estimate of geometric flows of Hermitian metrics (Marco Gallo and Luigi Vezzoni, 2026)8Gallo 2026 Chern-Ricci flow on Kato surfaces (Daniele Angella and Mauricio Corrêa, 2026)3Angella 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. The Chern-Ricci flow

    Valentino Tosatti and Ben Weinkove

    Topics Generalized & G₂ flows · Shared terms “Chern Ricci”, “Hermitian”

  2. Leafwise flat forms on Inoue-Bombieri surfaces

    Daniele Angella and Valentino Tosatti

    Topics Generalized & G₂ flows · Same author Daniele Angella · Shared terms “Inoue”, “Chern Ricci”

  3. Chern-Ricci flow on Kato surfaces

    Daniele Angella and Mauricio Corrêa

    Topics Generalized & G₂ flows · Same author Daniele Angella · Shared terms “Chern Ricci”, “Hermitian”

  4. Hermitian metrics on complex non-Kähler manifolds

    Daniele Angella

    Topics Generalized & G₂ flows · Same author Daniele Angella · Shared terms “Chern Ricci”, “Hermitian”

  5. Weak Solutions of the Chern-Ricci flow on compact complex surfaces

    Xiaolan Nie

    Topics Generalized & G₂ flows · Shared terms “Chern Ricci”, “Hermitian”

  6. The Chern-Ricci flow on primary Hopf surfaces

    Gregory Edwards

    Topics Generalized & G₂ flows · Shared terms “Chern Ricci”, “Hopf”, “VII”

  7. On Gauduchon connections with Kähler-like curvature

    Daniele Angella, Antonio Otal, Luis Ugarte et al.

    Topics Generalized & G₂ flows · Same author Daniele Angella · Shared terms “Chern”, “Hermitian”

  8. On the Calabi estimate of geometric flows of Hermitian metrics

    Marco Gallo and Luigi Vezzoni

    Topics Generalized & G₂ flows · Shared terms “Chern Ricci”, “Hermitian”

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) 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)

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.