Long-time existence of the pluriclosed flow on some fibrations

Abstract

We prove long-time existence of the pluriclosed flow on certain compact quotients of Lie groups for non-invariant initial data, as well as on some holomorphic principal torus bundles over nonpositively curved Kähler manifolds. In particular, our results cover the cases of nilmanifolds and almost-abelian solvmanifolds, and provide a new proof of the long-time existence of the pluriclosed flow on certain complex surfaces, originally established by Garcia-Fernandez, Jordan, and Streets. These results follow from a general theorem on holomorphic submersions, which is of independent interest and, in particular, also implies the long-time existence of the pluriclosed flow on Oeljeklaus-Toma manifolds, as proved by Streets and Wang.