Abstract
We analyze supersymmetric solutions of M-theory based an a seven-dimensional internal space with $\mathrm{S}\mathrm{U}(3)$ structure and a four-dimensional maximally symmetric space. The most general supersymmetry conditions are derived and we show that a nonvanishing cosmological constant requires the norms of the two internal spinors to differ. We find explicit local solutions with singlet flux and the space being a warped product of a circle, a nearly K\"ahler manifold and ${\mathrm{A}\mathrm{d}\mathrm{S}}_{4}$. The embedding of solutions into heterotic M-theory is also discussed.
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