Spinor represantation of successor curves in Euclidean space

This thesis consists of five chapters. The first chapter consists of the introduction. In this section, literature has been given. In the second chapter, basic definitions and theorems in Euclidean space have been expresed. In the third section, at the Materials and Methods part, the successor curves have been explained in detail. Then, basic information about spinors has been mentioned. The fourth section is the original part of this thesis. In this section, the spinor formulations of successor curves of given a unit speed curve in three dimensional Euclidean space has been investigated. For this, first of all, two spinors corresponding to the unit speed curve and a successor curve of this curve have been taken separately. Then, by using the relationships between the unit speed curve and its successor curve, the relationships between two spinors corresponding to these curves have been obtained. Moreover, some spinor equations of spinors corresponding to these curves have been expressed with theorems and results. In addition, some geometric interpretations for these spinors have been given with the results. Then, by taking the successor curve as a helix curve, the spinor representation of the successor helix curve has been characterized with some theorems. Finally, two examples have been obtained. In the fifth section, results and recommendations have been given.