A Parabolic Flow of Pluriclosed Metrics

We define a parabolic flow of pluriclosed metrics. This flow is of the same family introduced by the authors in [11]. We study the relationship of the existence of the flow and associated static metrics topological information on the underlying complex manifold. Solutions to the static equation are automatically Hermitian-symplectic, a condition we define herein. These static metrics are classified on K3 surfaces, complex toroidal surfaces, nonminimal Hopf surfaces, surfaces of general type, and Class VII surfaces. To finish we discuss how the flow may potentially be used to study the topology of Class VII surfaces.