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 [15]. We study the relationship of the existence of the flow and associated static metrics to 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.