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.

• Frobenius theorem (differential topology) – On finding a maximal set of solutions of a system of first-order homogeneous linear PDEs
• Sub-Riemannian manifold – Type of generalization of a Riemannian manifold