  In this paper, we investigate the geometries associated with 3-forms of
various orbital types on a symplectic 6-manifold. We show that there are
extremely rich geometric structures attached to certain unstable 3-forms
arising naturally from degeneration of Calabi-Yau structures, which in turn
provides us a new perspective towards the SYZ conjecture. We give concrete
examples and demonstrate that the limiting behavior of the Type IIA flow can be
used to detect canonical geometric structures on symplectic manifolds.
