Frobenius Integrability (overdetermined Differential Systems)
A differential system is said to be completely integrable in the Frobenius sense if the space on which it is defined has a foliation by maximal integral manifolds. The Frobenius theorem states that a system is completely integrable if and only if it generates an ideal that is closed under exterior differentation. (See the article on integrability conditions for differential systems for a detailed discussion of foliations by maximal integral manifolds.)
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