Analysis of curves by means of D-homothetic transformations and contact structures of (2n+1)-dimensional sphere

This thesis, consisting of four chapters, explores the D-homothetic transformations of Sasakian manifolds and examines their effects on Frenet curves. The Sasakian structure of the sphere is studied in detail, and the obtained results are applied to Legendre and slant geodesic curves on the 3-dimensional unit sphere. Additionally, examples are provided on a Sasakian manifold other than the sphere. The first chapter is the introduction. In the second chapter, the fundamental concepts and definitions that will be used in the following chapters are presented. The third chapter is the main part of the thesis. In this chapter, D-homothetic transformations of Sasakian manifolds are defined, and their effects on curves are examined. The obtained results are applied to various Sasakian manifolds. In the final chapter, a general evaluation is made and it is discussed how the results of this thesis can guide future studies.