The Chern-Ricci flow on Oeljeklaus-Toma manifolds

Abstract

We study the Chern-Ricci flow, an evolution equation of Hermitian metrics, on a family of Oeljeklaus-Toma (OT-) manifolds which are non-Kähler compact complex manifolds with negative Kodaira dimension. We prove that, after an initial conformal change, the flow converges, in the Gromov-Hausdorff sense, to a torus with a flat Riemannian metric determined by the OT-manifolds themselves.

22pages,correct some typos

References in corpus (3)

• The Kähler-Ricci flow on surfaces of positive Kodaira dimension
• Inoue surfaces and the Chern-Ricci flow
• Collapsing of Products Along the Kähler-Ricci Flow

Cited by in corpus (7)

• The Anomaly flow over Riemann surfaces
• Regularizing properties of Complex Monge-Ampère flows II: Hermitian manifolds
• The Chern-Ricci flow and holomorphic bisectional curvature
• A parabolic Monge-Ampère type equation of Gauduchon metrics
• Leafwise flat forms on Inoue-Bombieri surfaces
• Regularity of Degenerate Hessian Equation
• The continuity equation for Hermitian metrics: Calabi estimates, Chern scalar curvature and Oeljeklaus-Toma manifolds