Subbundle

Inmathematics, a subbundle ${\displaystyle U}$ of a vector bundle ${\displaystyle V}$ on a topological space ${\displaystyle X}$ is a collection of linear subspaces ${\displaystyle U_{x}}$of the fibers ${\displaystyle V_{x}}$of${\displaystyle V}$at${\displaystyle x}$in${\displaystyle X,}$ 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 (oftangent vectors).

If a set of vector fields ${\displaystyle Y_{k}}$ span the vector space ${\displaystyle U,}$ and all Lie commutators ${\displaystyle \left[Y_{i},Y_{j}\right]}$ are linear combinations of the ${\displaystyle Y_{k},}$ then one says that ${\displaystyle U}$ is an involutive distribution.

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