Type 2 paf and its application to Tzitzeica and Smarandache curves

This thesis includes six sections. The first section is an introduction devoted to the literature knowledge. In the second section, basic mathematical and some physical concepts thought to be useful for the original part of the thesis are mentioned. In the third section, the construction process of the Positional Adapted Frame which has importance for this study is explained. Fourth section is the first of the sections which constitute the original part of our study. Type 2-Positional Adapted Frame which constitutes the basis of our study is introduced and the angular velocity vector is given according to this frame in this section. In fifth section, some characterizations related to Tzitzeica curves in 3-dimensional Euclidean space are given and some results are obtained for the spherical Tzitzeica curves. In the last section, the trajectories generated by special Smarandache curves according to the Type 2- Positional adapted Frame and the Frenet elements of these trajectories are emphasized.