  We consider compactifications induced by the gravitino field of eleven
dimensional supergravity. Such compactifications are not trivial in the sense
that the gravitino profiles are not related to pure bosonic ones by means of a
supersymmetry transformation. The basic property of such backgrounds is that
they admit $\psi$-torsion although they have vanishing Riemann tensor. Thus,
these backgrounds may be considered also as solutions of the teleparallel
formulation of supergravity. We construct two classes of solutions, one with
both antisymmetric three-form field, gravity and gravitino and one with only
gravity and gravitino. In these classes of solutions, the internal space is a
parallelized compact manifold, so that it does not inherit any cosmological
constant to the external spacetime. The latter turns out to be flat Minkowski
in the maximally symmetric case. The elimination of the cosmological constant
in the spontaneously compactified supergravity seems to be a generic property
based on the trading of the cosmological constant for parallelizing torsion.
