subbundle

{{Short description|Mathematical collection}}

File:Subbundle.png

In mathematics, a subbundle $L$ of a vector bundle $E$ over a topological space $M$ is a collection of linear subspaces $L\_x$of the fibers $E\_x$ of $E$ at $x$ in $M,$ 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 $N\_x$ of $x\; \backslash in\; M$, a set of vector fields $Y\_k$ span the vector spaces $L\_y,\; y\; \backslash in\; N\_x,$ and all Lie commutators $\backslash left[Y\_i,\; Y\_j\backslash right]$ are linear combinations of $Y\_1,\; \backslash dots,\; Y\_n$ then one says that $L$ is an involutive distribution.