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A parabolic flow of pluriclosed metrics. (English) Zbl 1198.53077
Summary: We define a parabolic flow of pluriclosed metrics. 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, non-minimal 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.

MSC:
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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