Embedding into manifolds with torsion

We introduce a class of special geometries associated to the choice of a differential graded algebra contained in ${\Lambda^*\mathbb{R}^n}$ . We generalize some known embedding results, that effectively characterize the real analytic Riemannian manifolds that can be realized as submanifolds of a Riemannian manifold with special holonomy, to this more general context. In particular, we consider the case of hypersurfaces inside nearly-K?hler and ??-Einstein?CSasaki manifolds, proving that the corresponding evolution equations always admit a solution in the real analytic case.