Frobenius theorem on Pfaffian systems
A theorem on the conditions for a system of Pfaffian equations to be completely integrable, or (in geometrical terms) on conditions under which a given field of $n$-dimensional tangent subspaces on a differentiable manifold is the tangent field of some foliation. For several equivalent formulations of the Frobenius theorem, see the articles Involutive distribution; Cauchy problem; for a version with minimum differentiability requirements see . The name of the theorem is connected with the account of it in , but does not accord with the information given there about its history.
|||G. Frobenius, "Ueber das Pfaffsche Problem" J. Reine Angew. Math. , 82 (1877) pp. 230–315|
|||P. Hartman, "Ordinary differential equations" , Birkhäuser (1982) MR0658490 Zbl 0476.34002|
Frobenius theorem on Pfaffian systems. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Frobenius_theorem_on_Pfaffian_systems&oldid=41955