Absolute contact differentiation on submanifolds of Cartan spaces

We introduce the general concept of higher order absolute contact differentiation that is based on the idea of semiholonomic contact elements. We clarify how the moving frame method leads to the coordinate functions of the field of r-th order contact elements on a submanifold of Klein space and of the r-th absolute contact differential of a submanifold of Cartan space. We point out that the standard geometric objects of submanifolds are defined on contact elements, so that they are of universal character. In examples, we use heavily the concept of universal horizontal and vertical bundle over contact elements.