2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223357This 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.Differential GeometrySymplectic Geometry53C, 28Atext