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.
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A rank- distribution on a smooth manifold is a rank- vector subbundle of its tangent bundle. It is involutive when the Lie bracket of vector fields of any two local sections is again a section.