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 $\tfrac{1}{1+t}\omega_t$ 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.