  We consider a smooth boundary b\Omega which is q-convex in the sense that its
Levi-form has positive trace on every complex q-plane. We prove that b\Omega is
tangent of infinite order to the complexification of each of its submanifolds
which is complex tangential and of finite bracket type. This generalizes
Diederich-Fornaess [Annals 1978] from pseudoconvex to q-convex domains. We also
readily prove that the rows of the Levi-form are (1/2)-subelliptic multipliers
for the di-bar-Neumann problem on q-forms (cf. Ho [Math. Ann. 1991]). This
allows to run the Kohn algorithm of [Acta Math. 1979] in the chain of ideals of
subelliptic multipliers for q-forms. If b\Omega is real analytic and the
algorithm stucks on q-forms, then it produces a variety of holomorphic
dimension q, and in fact, by our result above, a complex q-manifold which is
not only tangent but indeed contained in b\Omega. Altogether, the absence of
complex q-manifolds in b\Omega produces a subelliptic estimate on q-forms.
