Prolongations of Connections to Tangential Fibre Bundles of Higher Order

In the previous paper [3] we have studied the prolongations of G-structures to tangent bundles of higher order. The purpose of the present paper is to study the prolongations of connections to tangential fibre bundles of higher order, and to generalize the results due to S. Kobayashi [1] for the case of usual tangent bundle —— in fact, the arguments in [1] will be, in a sense, more or less simplified and clarified by using the notion of tangent bundles of higher order. In addition, as a consequence of our results, we shall obtain the prolongations of linear (affine) connections to tangent bundles of higher order.