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We consider warp compactifications of M-theory on 7-manifolds in the presenceof 4-form fluxes and investigate the constraints imposed by supersymmetry. Aslong as the 7-manifold supports only one Killing spinor we infer from theKilling spinor equations that non-trivial 4-form fluxes will necessarily curvethe external 4-dimensional space. On the other hand, if the 7-manifold has atleast two Killing spinors, there is a non-trivial Killing vector yielding areduction of the 7-manifold to a 6-manifold and we confirm that 4-form fluxescan be incorporated if one includes non-trivial SU(3) structures.Comment: 13 pages, Latex; minor changes & add reference

Fluxes in M-theory on 7-manifolds andGstructures