As on arXiv
Abstract
In this paper, we study the -Gauduchon Ricci-flat condition under the Chern-Ricci flow. In this setting, we provide examples of Chern-Ricci flow on compact non-Kähler Calabi-Yau manifolds which do not preserve the -Gauduchon Ricci-flat condition for . The approach presented generalizes some previous constructions on Hopf manifolds. Also, we provide non-trivial new examples of balanced non-pluriclosed solution to the pluriclosed flow on non-Kähler manifolds. Further, we describe the limiting behavior, in the Gromov-Hausdorff sense, of geometric flows of Hermitian metrics (including the Chern-Ricci flow and the pluriclosed flow) on certain principal torus bundles over flag manifolds. In this last setting, we describe explicitly the Gromov-Hausdorff limit of the pluriclosed flow on principal -bundles over the Fano threefold .
Comments: 26 pages
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.
-
Levi-Civita Ricci-flat metrics on non-Kähler Calabi-Yau manifolds
Topics Ricci-flat & Calabi–Yau, Generalized & G₂ flows, Limit spaces & RCD · Same author Eder M. Correa · Shared terms “Hopf manifolds”, “previous constructions”, “Chern Ricci”
-
Pluriclosed flow on Oeljeklaus-Toma manifolds
Topics Generalized & G₂ flows, Limit spaces & RCD, Kähler geometry · Shared terms “pluriclosed flow”, “Gromov Hausdorff”
-
The Chern-Ricci flow
Topics Generalized & G₂ flows · Shared terms “Chern Ricci”, “Hermitian metrics”
-
Chern-Ricci flow on Kato surfaces
Topics Generalized & G₂ flows, Limit spaces & RCD · Shared terms “Chern Ricci”, “Gromov Hausdorff”, “Hermitian metrics”
-
On the Calabi estimate of geometric flows of Hermitian metrics
Topics Generalized & G₂ flows, Kähler geometry · Shared terms “Hermitian metrics”, “Chern Ricci”, “geometric flows”
-
Derivative estimates of pluriclosed flow
Topics Generalized & G₂ flows, Kähler geometry · Shared terms “pluriclosed flow”, “Chern Ricci”, “Hermitian”
-
Some remarks on strong -structures with torsion
Topics Ricci-flat & Calabi–Yau, Generalized & G₂ flows · Shared terms “pluriclosed flow”, “Hermitian”
-
The parabolic quaternionic Calabi-Yau equation on hyperkähler manifolds
Topics Ricci-flat & Calabi–Yau, Generalized & G₂ flows, Kähler geometry · Shared terms “Chern Ricci”
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
- 6C.11Optimal Transport and Ricci Curvature
Kantorovich duality, Wasserstein geometry, the heat equation as a gradient flow of entropy, displacement convexity, and Ricci curvature as convexity, from Lott–Sturm–Villani to McCann–Topping and the reduced volume.
- 9B.4Convergence of Manifolds
Gromov–Hausdorff and Cheeger–Gromov convergence, and the compactness theorem.
- 11B.3Compactness of Ricci Flows
Hamilton’s compactness theorem and the missing injectivity radius bound.