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 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.

A REPORT ON GAUGE INVARIANT FORMS AND VARIATIONAL PROBLEMS ON THE BUNDLE OF CONNECTIONS OF A PRINCIPAL U(1)-BUNDLE AND ON ASSOCIATED VECTOR BUNDLES

Basic results on gauge invariance of differential forms on the bundle of connections of an arbitrary principal U(1)-bundle and its associated bundles, are reviewed in terms of the underlying geometry to such bundles, within the framework of classical electromagnetism.