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Subbundle

Mathematical collection

Wikipedia contributorsAdapted for Fathomly · View authors
1 min read
Source updated August 27, 2026
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In mathematics, a subbundle L of a vector bundle E over a topological space M is a subset of E such that for each x in M, the set L_{x}, the intersection of the fiber E_{x} with L, is a vector subspace of the fiber E_{x} so that L is a vector bundle over M in its 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\in M, a set of vector fields Y_{k} span the vector spaces L_{y},y\in N_{x}, and all Lie commutators \left[Y_{i},Y_{j}\right] are linear combinations of Y_{1},\dots ,Y_{n} then one says that L is an involutive distribution.

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This article is adapted from the Wikipedia article “Subbundle”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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