symp-foliations

In dimension 3 it is known, due to Eliashberg-Thurston, that any foliation can be C0-approximated by a positive and a negative contact structure. Is the same true in higher dimensions for a symplectic foliation?

In dimension 3 tautness of the foliation implies tightness of the contact structure. In higher dimensions, being strong symplectic implies that any approximation (if it exists) is fillable and thus tight as well.

(A. Mori) In higher dimensions one can provide an alternate definition of confoliation: We say that a pair (\alpha,\tau) is a twisted contact structure, with \alpha a 1-form and \tau a 2-form, if d\alpha+\tau is non-degenerate along ker(alpha). Then, we will say that \alpha is a confoliation if there is a linear family \tau_x, x in (0,1], with (\alpha,\tau_x) twisted contact. In particular, this implies that αΛ(dα)^n is non-negative. One particular example of such a confoliation is the symplectic foliation considered by Mitsumatsu in S5.