Subbundle Explained

In mathematics, a subbundle

U of a vector bundle V on a topological space X is a collection of linear subspaces U _{x} of the fibers V _{x} of V at x in X, 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 a set of vector fields

Y _{k} span the vector space U, and all Lie commutators \left[Y _{i,} Y _{j\right]} are linear combinations of the Y _{k,} then one says that U is an involutive distribution