imported>Octavmitrea at 14:37, 5 December 2024

2024-12-05T14:37:58Z

New page

{{Short description|Mathematical collection}}
[[File:Subbundle.png|thumb|300px|A subbundle <math>L</math> of a vector bundle <math>E</math> over a topological space <math>M</math>.]]
In [[mathematics]], a '''subbundle''' <math>L</math> of a [[vector bundle]] <math>E</math> over a [[topological space]] <math>M</math> is a collection of [[linear subspace]]s <math>L_x</math>of the fibers <math>E_x</math> of <math>E</math> at <math>x</math> in <math>M,</math> 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 (differential geometry)|distribution]] (of [[tangent vector]]s).

If locally, in a neighborhood <math>N_x</math> of <math>x \in M </math>, a set of vector fields <math>Y_k</math> [[Linear span|span]] the vector spaces <math>L_y, y \in N_x,</math> and all [[Lie commutator]]s <math>\left[Y_i, Y_j\right]</math> are linear combinations of <math>Y_1, \dots, Y_n</math> then one says that <math>L</math> is an [[involutive distribution]].

== See also ==

* {{annotated link|Frobenius theorem (differential topology)}}
* {{annotated link|Sub-Riemannian manifold}}

{{Manifolds}}

[[Category:Fiber bundles]]

Subbundle - Revision history

imported>Octavmitrea at 14:37, 5 December 2024