In mathematics, a subbundle L {\displaystyle L} of a vector bundle E {\displaystyle E} over a topological space M {\displaystyle M} is a collection of linear subspaces L x {\displaystyle L_{x}} of the fibers E x {\displaystyle E_{x}} of E {\displaystyle E} at x {\displaystyle x} in M , {\displaystyle M,} 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 locally, in a neighborhood N x {\displaystyle N_{x}} of x ∈ M {\displaystyle x\in M} , a set of vector fields Y k {\displaystyle Y_{k}} span the vector spaces L y , y ∈ N x , {\displaystyle L_{y},y\in N_{x},} and all Lie commutators [ Y i , Y j ] {\displaystyle \left[Y_{i},Y_{j}\right]} are linear combinations of Y 1 , … , Y n {\displaystyle Y_{1},\dots ,Y_{n}} then one says that L {\displaystyle L} is an involutive distribution.