In this paper, we prove a theorem that answers this question. The theorem is known as frobenius theorem, and it says. Frobenius theorem a distribution on a manifold m is completely.
Frobenius' theorem is one of the supporting pillars of differential topology and the calculus on manifolds. In mathematics, frobenius' theorem states that a subbundle of the tangent bundle of a manifold is integrable if and only if it arises from a regular foliation. While the above examples were chosen so that we could verify easily whether or not they were the collection of tangent spaces to a manifold, in general this question is dicult to answer. Outline statement of the theorem. Proof of the perron frobenius theorem. Lawson, it is actually due to alfred clebsch and.
Abstract the main purpose of this talk is to present the frobenius theorem. The theorem is named after ferdinand georg frobenius, but according to. Let m be a c manifold, x a vector eld on m and p m. The only if part, an existence theorem for foliations, turns analysis into geometry.