ON THE GAUGE VERSION OF EXPONENTIAL MAP

摘要

Let P(M, G) be a principal bundle, F be a principal connection on P and A be a classical connection on M. For every u E P, we construct a local map exp u r' A : TuP —> P. Then we clarify how these maps can be used for finding all natural operators transforming (F, A) into a principal connection of the r-th principal gauge prolongation W rP of P. We also deduce that expr' A coincides with the exponential map of a classical connection on P.