KK-monopoles and G-structures in M-theory/type IIA reductions

We argue that M-theory/massive IIA backgrounds including KK-monopoles are suitably described in the language of G-structures and their intrinsic torsion. To this end, we study classes of minimal supergravity models that admit an interpretation as twisted reductions in which the twist parameters are not restricted to satisfy the Jacobi constraints ωω = 0 required by an ordinary Scherk-Schwarz reduction. We first derive the correspondence between four-dimensional data and torsion classes of the internal space and, then, check the one-to-one correspondence between higher-dimensional and four-dimensional equations of motion. Remarkably, the whole construction holds regardless of the Jacobi constraints, thus shedding light upon the string/M-theory interpretation of (smeared) KK-monopoles.