Paper · Jul 24, 2024
The behavior of the second Ricci flow on complex parallelizable manifolds
As on arXiv
Abstract
We study the flow of Hermitian metrics governed by the second Chern-Ricci form on a compact complex manifolds. The flow belongs to the family of Hermitian curvature flows introduced by Streets and Tian and it was considered by Lee in order to study compact Hermitian manifolds with almost negative Chern bisectional curvature. We show a regularity result on compact complex parallelizable manifolds and we prove that Chern-flat metrics are dynamically stable.
Comments: New version of "The behavior of the Hermitian curvature flow with Q=0 on complex parallelizable manifolds", 14 pages. To appear in Commun. Contemp. Math
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.
-
On the Calabi estimate of geometric flows of Hermitian metrics
Topics Generalized & G₂ flows · Same author Luigi Vezzoni · Shared terms “Hermitian metrics”, “Hermitian curvature”, “Chern Ricci”
-
The Chern-Ricci flow
Topics Generalized & G₂ flows · Shared terms “Chern Ricci”, “Hermitian metrics”, “complex manifold”
-
The parabolic quaternionic Calabi-Yau equation on hyperkähler manifolds
Topics Generalized & G₂ flows · Same authors Lucio Bedulli, Luigi Vezzoni · Shared terms “Chern Ricci”
-
Hermitian metrics on complex non-Kähler manifolds
Topics Generalized & G₂ flows · Shared terms “Hermitian metrics”, “compact complex”, “Chern”
-
Regularity of solutions to Monge–Ampère equations on compact Hermitian manifolds
Topics Generalized & G₂ flows · Shared terms “compact Hermitian”, “Hermitian manifolds”, “Chern”
-
Strong Uniqueness for Instantaneously Complete Chern-Ricci Flow
Topics Generalized & G₂ flows · Shared terms “Chern Ricci”, “Hermitian”, “complex manifold”
-
Chern holonomy under the first and second Chern–Ricci flows
Topics Generalized & G₂ flows · Shared terms “Chern”, “compact complex”, “complex manifold”
-
Dynamical stability of Pluriclosed and Generalized Ricci solitons
Topics Generalized & G₂ flows · Shared terms “dynamically stable”, “Chern”
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.
In the guidebook
- 5A.5Uniformization and the Two-Dimensional Ricci Flow
Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.
- 10A.12Curve Shortening and Minimal Discs
How loops shrink under curvature, how the discs they bound lose area, and Perelman's extinction estimate.
- 11A.1The Equation and Its First Solutions
A heat equation for the metric: spheres, cylinders and scaling.