A parabolic flow of pluriclosed metrics

Details A parabolic flow of pluriclosed metrics A parabolic flow of pluriclosed metrics

2009-03-25

arxiv.org/abs/0903.4418v2

Mathematics

Differential Geometry

Scientific paper

We define a parabolic flow of pluriclosed metrics. This flow is of the same family introduced by the authors in \cite{ST}. 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 $\seven^+$ surfaces. To finish we discuss how the flow may potentially be used to study the topology of Class $\seven^+$ surfaces.

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