On certain geometrical structures on the bundle of jets of differentiable mappings (Q1916556)

Within the bundle of 1-jets of differentiable mappings, the author describes the lifts of functions, 1-forms and vector fields, the tensor product of lifts, the horizontal lifts of vector fields and 1-forms -- with respect to a given linear connection, the prolongation of Riemannian metrics, and the horizontal and synectic lifts of linear connections. Finally, a characterization for the infinitesimal projective transformation of the synectic lift of a torsion-free linear connection is provided.