The Geometry of Tangent Bundles: Canonical Vector Fields. (14th April 2013)

• Record Type: Journal Article
• Authors: Li, Tongzhu; Krupka, Demeter
• Other Names: Fino Anna Academic Editor.
• Is Part Of: Geometry. Volume 2013(2013)
• Publication Date: 2013-04-14
• Subjects: Geometry -- Periodicals; Geometry; Periodicals; 516
• DOI: 10.1155/2013/364301
• Languages: English
• ISSNs: 2314-422X

Abstract

Abstract : 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.