Integrable distribution

Definition

A distribution on a differential manifold is said to be integrable if, for any point on the differential manifold, there is an integral manifold for the distribution containing that point.

Facts

Existence of foliations

Further information: Frobenius theorem

According to Frobenius theorem, a distribution is integrable if and only if it arises from a foliation. A foliation is a partition of the entire manifold into maximal integral manifolds for the distribution.