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Tangent Bundle

Basic definition

In topology, a tangent bundle of a given manifold is a new manifold that consists of the tangent spaces for each point pasted together in a continuous fashion.

Detailed definition

Every smooth manifold M has a tangent bundle T M, which consists of the tangent space T M_p at all points p in M. Since a tangent space T M_p is the set of all tangent vectors to M at p, the tangent bundle is the collection of all tangent vectors, along with the information of the point to which they are tangent.

Related terms

calculus | coordinate chart | cotangent bundle | directional derivative | Euclidean space | Jacobian | manifold | tangent bundle section | tangent space | tangent vector | vector field | vector space

Educational grade level

graduate school level

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