Double Tangent Bundle

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Beschreibung

In mathematics, particularly differential topology, the double tangent bundle or the second tangent bundle refers to the tangent bundle T2M=T(TM) of the tangent bundle TM of a smooth manifold M. The double tangent bundle arises in the study of connections and second order ordinary differential equations, i.e. (semi)spray structures on smooth manifolds. The double tangent bundle is closely related to the second order jet bundle, which is an object specifically designed to hold the "2nd order derivative information" of smooth functions on smooth manifolds. Given a smooth map f : M to N there is an induced 1st-order derivative map Tf : TM to TN and so also a 2nd order derivative map T^2 f : T^2 M to T^2 N. The Lie Bracket of two vector fields on a manifold also has a formulation in terms of the double tangent bundle.

Produktinformationen

Titel:

Double Tangent Bundle

Untertitel:

Mathematics, Differential topology, Tangent bundle, Differentiable manifold, Connection (vector bundle), Spray (mathematics), Jet bundle, Lie bracket of vector fields, Vector field

Editor:

Frederic P. Miller

Agnes F. Vandome

John McBrewster

EAN:

9786130618476

ISBN:

978-613-0-61847-6

Format:

Fachbuch

Herausgeber:

OmniScriptum