Principal bundle structure on jet prolongations of frame bundles

In this paper, we introduce the structure of a principal bundle on the r-jet prolongation J (r) FX of the frame bundle FX over a manifold X. Our construction reduces the well-known principal prolongation W (r) FX of FX with structure group G (n) (r) . For a structure group of J (r) FX we find a suitable subgroup of G (n) (r) . We also discuss the structure of the associated bundles. We show that the associated action of the structure group of J (r) FX corresponds with the standard actions of differential groups on tensor spaces.