The Geometry of Tangent Bundles : Canonical Vector Fields

Abstract EN

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.