Symplectic curvature flow

Abstract

We introduce a parabolic flow of almost Kahler structures, providing an approach to constructing canonical geometric structures on symplectic manifolds. We exhibit this flow as one of a family of parabolic flows of almost Hermitian structures, generalizing our previous work on parabolic flows of Hermitian metrics. We exhibit a long time existence obstruction for solutions to this flow by showing certain smoothing estimates for the curvature and torsion. We end with a discussion of the limiting objects as well as some open problems related to the symplectic curvature flow.

Final version, to appear in Crelle's Journal

References in corpus (1)

• Regularity results for pluriclosed flow

Cited by in corpus (5)

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• A parabolic flow of balanced metrics
• A Curvature Flow Unifying Symplectic Curvature Flow And Pluriclosed Flow
• On distinguished orbits of reductive representations
• Cohomological properties of Hermitian symplectic threefolds