Subbundle

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title: "Subbundle" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["fiber-bundles"] description: "Mathematical collection" topic_path: "general/fiber-bundles" source: "https://en.wikipedia.org/wiki/Subbundle" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::summary Mathematical collection ::

::figure[src="https://upload.wikimedia.org/wikipedia/commons/4/4b/Subbundle.png" caption="A subbundle L of a vector bundle E over a topological space M."] ::

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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