Distribution (differential geometry)

In differential geometry, the term "distribution" refers to a smooth assignment of a subspace of the tangent space at each point of a manifold. More formally, given a smooth manifold \( M \), a distribution is a smooth assignment of a vector subspace \( D_p \) of the tangent space \( T_p M \) at each point \( p \in M \). Distributions are often used to study geometric structures, such as foliations and control systems.