Smarandache curves and ruled surfaces of spheri̇cal curves in dual Euclidean and dual Lorentzian spaces

This thesis consists of six chapters. In the first chapter, basic definitions and elementary theorems of dual space are given. In the second chapter, firstly Smarandache curves of a dual spherical curve is given in the dual space . Furthermore, the theorems and proofs which characterize relations between these curves and the relationships between ruled surfaces corresponding to dual spherical curves are introduced. In the third chapter, basic definitions and theorems, geometry of dual curves lying on the dual Hyperbolic and Lorentzian spheres are given in dual Lorentzian space and ruled surfaces corresponding these dual curves are introduced in In the fourth, fifth and sixth chapters, respectively, Smarandache curves of spacelike curves lying on hyperbolic unit sphere , timelike curves lying on lorentizan unit sphere and spacelike curves lying on lorentizan unit sphere are given. Theorems which characterize relations between dual spherical curves and using E. Study mapping, the relationships between ruled surfaces corresponding to these dual spherical curves are obtained.