# Article

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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.

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