Canonical connections on a rigged bundle and generalized Finsler spaces (Q1920861)

The author associates to a given bundle endowed with a vector field transversal to the fibers (rigged bundle) a series of connections; the most important of them is a connection on the base manifold which provides a parallel translation of vectors over the base, having as geodesics exactly the dynamical trajectories (the trajectories of motion of a material point under the action of a field of forces dependent on the direction). Also, it is shown that specifying a vector field transversal to the fibers of the bundle is equivalent to furnishing the base of the bundle with a structure of a generalized Finsler space endowed with a field of forces dependent on the direction.