  This article presents the further steps of the previously done studies taking
into consideration the k-th order extensions of a complex manifold. In the
previous studies higher order vertical and complete lifts of structures on the
complex manifold were introduced. Presently, k-th extended spaces of a product
manifold have been set and the higher order vertical, complete, complete-
vertical and horizontal lifts of geometric structures on the product manifold
have been presented.
