Smarandache curves created with the help of sabban frames of archimedean spirals on the surface of unit sphere

This thesis consists of six chapters. In the first chapter, general information about the Sabban frame and Smarandache curves used in the thesis is given and the studies in the literature on these subjects are summarized. In the second chapter, definitions and theorems of basic concepts used in the thesis such as Euclidean space, differentiable curve, arc length, Sabban frame of a curve on the surface of unit sphere and Smarandache curves constructed with the help of this frame are given. In the third chapter, geodesic curvatures of the γt, γd, td, and γtd Smarandache curves constructed using the Sabban vectors of a non-unit speed curve on the surface of unit sphere are found. In the fourth chapter, the spherical Archimedean spiral is introduced and the Sabban frame of the Archimedean spiral on the surface of unit sphere is established. In addition, the apparatus of Sabban frame of the Viviani curve, which is a special case of the spherical Archimedes spiral, are also determined. In the fifth chapter, Smarandache curves belonging to the Sabban frame of the Archimedean spirals on the surface of unit sphere and the special case of these curves, the Viviani curve, are defined. Sabban vectors and geodesic curvatures of the defined Smarandache curves are found. In the sixth chapter, the results obtained in the thesis and suggestions for future studies are given. Third, fourth and fifth chapters of the thesis are original. The curves in the figures of the thesis are drawn by using the Maple program.