Symplectic curvature flow

Details Symplectic curvature flow Symplectic curvature flow

2010-12-09

arxiv.org/abs/1012.2104v3

Mathematics

Differential Geometry

Some errors corrected, Theorem 1.10 extended to all dimensions

Scientific paper

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.

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