Invariant lagrangians on the vertically adapted linear frame bundle

Abstract

For the bundle of linear frames LM of a manifold M, diffeomorphism invariance on the vertically adapted linear frame bundle L π (LM) and its infinitesimal counterpart, invariance under the natural representation of vector fields of M, are analyzed. Furthermore, the structure of the vector-field-invariant Lagrangians on L π (LM) is determined. © 2011 Springer-Verlag Berlin Heidelberg.