Yo,Yr,Yn darboux slant helices and osculating, rectifying, normal spherical indicator curves

This thesis study consists of six chapters. The first chapter is the introduction of the thesis. In this section, literature information about special curves and special curves on the surface and brief information about what has been done in this thesis are given. In the second chapter, the basic concepts of the theory of curves and surfaces in 3-dimensional Euclidean space, the basic concepts and theorems of the osculating Darboux frame, the rectifying Darboux frame and the normal Darboux frame are given. The third, fourth and fifth chapters constitute the original parts of the thesis. In the third chapter, Darboux slant helis is defined on the surface and a curve is drawn according to the osculator Darboux frame. The condition of being Darboux slant helix is given. In addition, the global indicator curves of the unit vector fields of the osculator Darboux frame are defined and the equations of the Frenet elements of the global indicator curves related to the osculator Darboux frame are given. In the fourth chapter, Darboux slant helis is defined on the surface and the condition for a curve to be Darboux slant helis according to the rectifying Darboux frame is given. In addition, the global indicator curves of the unit vector fields of the rectifying Darboux frame are defined and the equations of the Frenet elements of the global indicator curves based to the rectifying Darboux frame are given. In the fifth chapter, Darboux slant helis is defined on the surface and a curve is drawn according to the normal Darboux frame. The condition of being Darboux slant helix is given. In addition, the global indicator curves of the unit vector fields of the normal Darboux frame are defined and the equations of the Frenet elements of the global indicator curves based to the normal Darboux framework are given. In the sixth section, result and recommendations are given.