Cotangent bundle: Difference between revisions
(New page: ==Definition== The '''cotangent bundle''' of a differential manifold is the dual bundle to its tangent bundle. In other words, it is a bundle whose fiber at every point is the dua...) |
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==Definition== | ==Definition== | ||
The '''cotangent bundle''' of a [[differential manifold]] is the dual bundle to its [[tangent bundle]]. In other words, it is a bundle whose fiber at every point is the dual vector space to the [[tangent bundle]]. | The '''cotangent bundle''' of a [[differential manifold]] is the dual bundle to its [[tangent bundle]]. In other words, it is a bundle whose fiber at every point is the dual vector space to the [[tangent bundle]]. | ||
==Facts== | |||
{{section of this bundle|differential 1-form|sheaf of differential 1-forms}} | |||
{{dual bundle|tangent bundle}} | |||
Latest revision as of 19:36, 18 May 2008
This article defines a basic construct that makes sense on any differential manifold
View a complete list of basic constructs on differential manifolds
Definition
The cotangent bundle of a differential manifold is the dual bundle to its tangent bundle. In other words, it is a bundle whose fiber at every point is the dual vector space to the tangent bundle.
Facts
Sections
A section of this bundle is termed a: differential 1-form
The sheaf of sections is termed the: sheaf of differential 1-forms
Dual bundle
The dual bundle to this vector bundle is termed the: tangent bundle