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