The Geometry of Tangent Bundles: Canonical Vector Fields | Zendy

Tongzhu Li | Zendy; Demeter Krupka | Zendy

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The Geometry of Tangent Bundles: Canonical Vector Fields

Author(s) -

Tongzhu Li,

Demeter Krupka

Publication year - 2013

Publication title -

geometry

Language(s) - English

Resource type - Journals

eISSN - 2314-4238

pISSN - 2314-422X

DOI - 10.1155/2013/364301

Subject(s) - vector field , tangent bundle , vector bundle , tangent vector , mathematics , vector valued differential form , vector potential , complex lamellar vector field , tangent , normal bundle , solenoidal vector field , canonical coordinates , field (mathematics) , frame bundle , lift (data mining) , mathematical analysis , tangent space , pure mathematics , geometry , physics , computer science , quantum mechanics , data mining , magnetic field , phase space , thermodynamics

A canonical vector field on the tangent bundle is a vector field defined by an invariant coordinate construction. In this paper, a complete classification of canonical vector fields on tangent bundles, depending on vector fields defined on their bases, is obtained. It is shown that every canonical vector field is a linear combination with constant coefficients of three vector fields: the variational vector field (canonical lift), the Liouville vector field, and the vertical lift of a vector field on the base of the tangent bundle

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