On the pluriclosed flow on Oeljeklaus-Toma manifolds

Abstract

We investigate the pluriclosed flow on Oeljeklaus-Toma manifolds. We parametrize left-invariant pluriclosed metrics on Oeljeklaus-Toma manifolds and we classify the ones which lift to an algebraic soliton of the pluriclosed flow on the universal covering. We further show that the pluriclosed flow starting from a left-invariant pluriclosed metric has a long-time solution ${\omega }_t$ which once normalized collapses to a torus in the Gromov-Hausdorff sense. Moreover the lift of $\frac{1}{1+t}{\omega }_t$ to the universal covering of the manifold converges in the Cheeger-Gromov sense to $({\mathbb{H}}^r\times {\mathbb{C}}^s,{\tilde{\omega }}_{\infty })$ where ${\tilde{\omega }}_{\infty }$ is an algebraic soliton.

arXiv comment22 pages. Minor revision