Do-Darboux slant helices, Dr-Darboux slant helices and Dn-Darboux slant helices on surface in 3-dimensional euclidean space

This thesis consists of six chapters. First chapter is introduction. In this chapter, literature review about special curves and special curves on surface and some information about this thesis is given. In chapter two, basic concepts of the theory of curves and surfaces in 3- dimensional Euclidian space are given. In chapter three, which is one of the original parts of the thesis, the Do-Darboux slant helices on the surface are examined. The osculator Darboux frame is defined and derivative formulas are found. Using this frame, the condition for a curve to be a Do-Darboux slant helix is given. Differential equation characterizations of Do-Darboux slant helices according to the osculator Darboux frame are given.Additionally, a method to obtain a Do-Darboux slant helix on a given surface in parametric and implicit form is found and examples are given. In chapter four, which is one of the original parts of the thesis, the Dr-Darboux slant helices on the surface are examined. The rectifying Darboux frame is defined and derivative formulas are found. Using this frame, the condition for a curve to be a Dr-Darboux slant helix is given. Differential equation characterizations of Dr-Darboux slant helices according to the rectifying Darboux frame are given. Later, a method to obtain a Dr-Darboux slant helix on a given surface in parametric and implicit form is found and examples are given. In chapter five, which is another original parts of the thesis, the Dn-Darboux slant helices on the surface are examined. The normal Darboux frame is defined and derivative formulas are found. Using this frame, the condition for a curve to be a Dn-Darboux slant helix is given. Differential equation characterizations of Dn-Darboux slant helices according to the normal Darboux frame are given. Finally, a method to obtain a Dn-Darboux slant helix on a given surface in parametric and implicit form is found and examples are given. In chapter six, results and recommendations are given.