3-structures with torsion

We find conditions which ensure the integrability of the canonical 3-dimensional distribution VV spanned by the Reeb vector fields of an almost 3-contact manifold, showing by an explicit counterexample that the normality of the structures does not necessarily imply the integrability of VV. Then we focus on those almost 3-contact metric manifolds for which VV is integrable and we define an appropriate notion of almost 3-contact metric connection with torsion. The geometry of an almost 3-contact manifold with torsion is then studied and put in relation with the well-known HKT-geometry.