Double Tangent Bundle
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SH699N47CPQ
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Details
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.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786130618476
- Editor Frederic P. Miller, Agnes F. Vandome, John McBrewster
- Sprache Englisch
- Größe H5mm x B220mm x T150mm
- Jahr 2010
- EAN 9786130618476
- Format Fachbuch
- ISBN 978-613-0-61847-6
- 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
- Gewicht 138g
- Herausgeber Alphascript Publishing
- Anzahl Seiten 80
- Genre Mathematik
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