The Chern-Ricci flow on Oeljeklaus-Toma manifolds

TL;DR

This paper investigates the behavior of the Chern-Ricci flow on Oeljeklaus-Toma manifolds, showing convergence to a flat torus in the Gromov-Hausdorff sense after an initial conformal change.

Contribution

It demonstrates the convergence of the Chern-Ricci flow on OT-manifolds to a flat torus, providing new insights into the flow's long-term behavior on non-Kähler manifolds.

Findings

Flow converges to a flat torus in Gromov-Hausdorff sense

Convergence occurs after an initial conformal change

Results apply to non-Kähler OT-manifolds with negative Kodaira dimension

Abstract

We study the Chern-Ricci flow, an evolution equation of Hermitian metrics, on a family of Oeljeklaus-Toma (OT-) manifolds which are non-K\"{a}hler 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.