The paper compiles the fundamental properties of lifts associated with extended affine connections and presents a relevant lemma. Furthermore, we extend a classical result of Yano and Ishihara to the k-th order lift, providing a higher-order formulation of complete lifts of wedge products and exterior derivatives. By applying lifting techniques to geometric structures on higher-order tangent bundles, we obtain new results for various standard classes of almost Hermitian manifolds. This study provides a unified perspective on standard classes of almost Hermitian manifolds, the theory of lifts, and the extensions of these structures.
