Subbundle

In mathematics, a subbundle

is a collection of linear subspaces

that make up a vector bundle in their own right.

In connection with foliation theory, a subbundle of the tangent bundle of a smooth manifold may be called a distribution (of tangent vectors).

If locally, in a neighborhood

, a set of vector fields

span the vector spaces

and all Lie commutators

are linear combinations of

is an involutive distribution.