Prolongations of G-Structures to Tangent Bundles of Higher Order

Source abstract

In the previous paper [4] we have studied the prolongations of G -structures to tangent bundles. The purpose of the present paper is to generalize the previous prolongations and to look at them from a wide view as a special case by considering the tangent bundles of higher order. In fact, in some places, the arguments and calculations in [4] are more or less simplified. Since the usual tangent bundle T(M) of a manifold M considers only the first derivatives or first contact elements of M , the previous paper contains, in most parts, only the calculation of derivatives of first order.