abstract: in the present paper, we give a necessary and sufficient condition for contact cr-warped product to be contact cr-product in kenmotsu space forms.

A method for constructing the syzygies of vector-valued bilinear forms is given. Explicit formulas for the generators of the relations among the invariant rational functions are listed. These formulas have applications in the geometry of Riemannian submanifolds and in CR geometry. 1 Preliminaries 1.