Subbundle Explained

In mathematics, a subbundle

of a vector bundle over a topological space is a subset of such that for each in the set , the intersection of the fiber with , is a vector subspace of the fiber so that is a vector bundle over in its 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

of , a set of vector fields span the vector spaces and all Lie commutators are linear combinations of then one says that is an involutive distribution