NATURAL PRINCIPAL CONNECTIONS ON THE PRINCIPAL GAUGE PROLONGATION OF A PRINCIPAL BUNDLE

摘要

Let Gamma be a principal connection on a principal bundle pi : P -> M and let Lambda be a linear connection on M. We describe all possible natural prolongations of Gamma, with respect to Lambda, to principal connections on the principal gauge prolongation W-r P of P. For r = 1, 2 we give the full classification, for r >= 3 we give a base of natural operators which generates all possible natural principal connections on W-r P.