Some special geometry in dimension six

summary:Motivated by the study of CR-submanifolds of codimension~$2$ in~$\bbfC^4$, the authors consider here a $6$-dimensional oriented manifold~$M$ equipped with a $4$-dimensional distribution. Under some non-degeneracy condition, two different geometric situations can occur. In the elliptic case, one constructs a canonical almost complex structure on~$M$; the hyperbolic case leads to a canonical almost product structure. In both cases the only local invariants are given by the obstructions to integrability for these structures. The local 'flat' models are a $3$-dimensional complex contact manifold and the product of two $3$-dimensional real contact manifolds, respectively