Abstract
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 G2 structure plays a crucial role in our
analysis, leading to the possibility of four-dimensional
compactifications with 
= 1 and = 2 supersymmetry.
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