The Mixed Curvatures on C N

The aim of the present paper is devoted to the investigation of some geometrical properties on the middle envelope in terms of the invariants of the third quadratic form of the normal line congruence C_N . The mixed middle curvature and mixed curvature on C_N are obtained in tenus of the Mean and Gauss curvatures of the surface of reference. Our study is considered as a continuation to Stephanidis (1], 2], 3], 4], 5]). The technique adapted here is based on the methods of moving frames and their related exteriour forms 6] and 7].