Subbundle

In mathematics, a subbundle L of a vector bundle E over a topological space M is a subset of E such that for each x in M, the set L_x, the intersection of the fiber E_x with L, is a vector subspace of the fiber E_x so that L is a vector bundle over M 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 N_x of x \in M , a set of vector fields Y_k span the vector spaces L_y, y \in N_x, and all Lie commutators \left[Y_i, Y_j\right] are linear combinations of Y_1, \dots, Y_n then one says that L is an involutive distribution.