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We analyze supersymmetric solutions of M-theory based an a seven-dimensionalinternal space with SU(3) structure and a four-dimensional maximally symmetricspace. The most general supersymmetry conditions are derived and we show that anon-vanishing cosmological constant requires the norms of the two internalspinors to differ. We find explicit local solutions with singlet flux and thespace being a warped product of a circle, a nearly-Kahler manifold and AdS_4.The embedding of solutions into heterotic M-theory is also discussed.Comment: 25 pages, Latex, references adde

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

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M-theory compactification, fluxes, andAdS4