We introduce a parabolic flow of almost Kähler 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.
|Original language||English (US)|
|Number of pages||43|
|Journal||Journal fur die Reine und Angewandte Mathematik|
|State||Published - Nov 1 2014|
All Science Journal Classification (ASJC) codes
- Applied Mathematics