Curvatures and potential of M–theory inD= 4 with fluxes and twist

We give the curvatures of the free differential algebra (FDA) of M--theorycompactified to D=4 on a twisted seven--torus with the 4--form flux switchedon. Two formulations are given, depending on whether the 1--form fieldstrengths of the scalar fields (originating from the 3--form gauge field$\hat{A}^{(3)}$) are included or not in the FDA. We also give the bosonicequations of motion and discuss at length the scalar potential which emerges inthis type of compactifications. For flat groups we show the equivalence of thispotential with a dual formulation of the theory which has the full $\rE_{7(7)}$symmetry.Comment: 14 pages, LaTeX source, typos correcte