Abstract
A theory of supermanifolds is developed in which a supermanifold is an ordinary manifold associated with a certain integrable second order G G -structure. A structure theorem is proved showing that every G ∞ {G^\infty } -supermanifold has a complete distributive lattice of foliations with flat affine leaves. Furthermore, an existence and uniqueness theorem for local flows of G ∞ {G^\infty } vector fields is proved.
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