Resumen de Generalizations of Frobenius' Theorem on Manifolds and Subcartesian Spaces

Jedrzej Sniatycki

• Let mathcal{F} be a family of vector fields on a manifold or a subcartesian space spanning a distribution D. We prove that an orbit O of mathcal{F} is an integral manifold of D if D is involutive on O and it has constant rank on O. This result implies Frobenius' theorem, and its various generalizations, on manifolds as well as on subcartesian spaces.