Supersymmetric M-theory compactifications with fluxes on seven-manifolds and G-structures

We consider Minkowski compactifications of M-theory on generic seven-dimensional manifolds. After analyzing the conditions on the four-form flux, we establish a set of relations between the components of the intrinsic torsion of the internal manifold and the components of the four-form flux needed for preserving supersymmetry. The existence of two nowhere vanishing vectors on any seven-manifold with G(2) structure plays a crucial role in our analysis, leading to the possibility of four-dimensional compactifications with N = 1 and N = 2 supersymmetry