On differential geometry of kinematic surfaces

This thesis consists of three chapters.In the first chapter, basic concepts about dual number, dual vectors, quaternions and dual quaternions are given.Basic definitions and theorems relavant with theory of curves and surfaces, which will be used in the thesis later on, have been discussed in chapter second.In the third chapter, definition of screw surface with fundametal forms, umbilical points, directions of curvature, Gauss and mean curvature are given. In addition Darboux and Frenet frames of images on a screw surface of curves on any surface are obtained. According to these frames the normal curvature, geodesic curvature and geodesic torsion of the curve were found. Then, the definition of the k-kinematic surface is given and it is obtained asymptotic directions, conjugate tangent vectors, Euler theorem and Dupin indicatrix for k-kinematic surfaces.