Table of Contents
Geometry
Volume 2013 (2013), Article ID 364301, 10 pages
http://dx.doi.org/10.1155/2013/364301
Research Article

The Geometry of Tangent Bundles: Canonical Vector Fields

1Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China
2Department of Mathematics, Faculty of Science, The University of Ostrava, 30. dubna 22, 70103 Ostrava, Czech Republic
3Department of Mathematics, La Trobe University, Melbourne, Bundoora, VIC 3086, Australia

Received 14 December 2012; Accepted 13 March 2013

Academic Editor: Anna Fino

Copyright © 2013 Tongzhu Li and Demeter Krupka. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.