Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 36 (1995), No. 1

Characterization of Higher-order Tangent Bundles

M. de Le\'on, J. A. Oubi\~na and M. Salgado

Tangent bundles of higher order are the framework on which the
higher order Lagrangian theories are developed. Moreover,
almost tangent manifolds of higher order have been shown to be
relevant in singular Lagrangian theories. The purpose of this
paper is to prove that under some global hypotheses a higher
order integrable almost tangent manifold is diffeomorphic to
the tangent bundle of the same order of some manifold.
An application to the reduction of singular Lagrangians is given.
MSC 1991: 53C15, 58F05, 70H35.