Subbundle

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 [Y_i,Y_j] are linear combinations of the Y_k, then one says that U is an involutive distribution.

See also

• Frobenius theorem (differential topology)
• Sub-Riemannian manifold

References

• Involutive Distribution, PlanetMath.org.