# Integrable distribution

From Diffgeom

Template:Distribution property

## 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.