Abstract
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 nr. For a structure group of J r FX we find a suitable subgroup of G nr. 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.
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