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Title: Subbundle  
Author: World Heritage Encyclopedia
Language: English
Subject: Frobenius theorem (differential topology), Vertical bundle, Hyperbolic set, CR manifold, Fiber bundles
Publisher: World Heritage Encyclopedia


In mathematics, a subbundle U of a vector bundle V on a topological space X is a collection of linear subspaces Ux of the fibers Vx 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 Yk span the vector space U, and all Lie commutators [Yi,Yj] are linear combinations of the Yk, then one says that U is an involutive distribution.

See also


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