Geometry of slant spherical curves in dual spaces

This thesis consists of five chapters. First chapter is introduction. In this chapter, literature review about the subject a dual curve which corresponds a ruled surface with using dual Darboux frame and some information about this thesis is given. In chapter two, preliminaries of Euclidean 3-space and ruled surface are given. In chapter three, preliminaries of Lorentzian 3-space and spacelike, timelike ruled surfaces are analyzed using frame of the ruled surface. In chapter four, preliminaries of dual space and by the aid of the E. Study Mapping, dual spherical curves that correspond to the ruled surfaces in Euclidean 3-space are given. Besides a slant dual curve is defined on unit dual sphere and some characterizations for a curve to be a slant dual curve are expressed. In chapter five, the geometry of slant dual curves on dual unit spheres are defined. Firstly in 5.1. unit dual curves and preliminaries of dual Lorentzian space are given. Then, in 5.3. slant dual hyperbolic curves, in 5.4. slant dual Lorentzian timelike curves and in 5.5. slant dual Lorentzian spacelike curves are investigated.