Mannheim curves in Euclidean space and spinors

This thesis consists of five chapters. The first chapter consist of the introduction. In this section, literature information has been given. In the second chapter, some basic definitions and theorems in Euclidean space that form the basis of this thesis has been given. In the third chapter, firstly, Mannheim curve pair in three-dimensional Euclidean space has been introduced. In addition, some characterizations of this curve pair have been given. Then, the spinor algebra has been briefly introduced and the spinor formulation of curves in three-dimensional Euclidean space has been given. The fourth chapter is the original part of this thesis. In this chapter, the expression of Frenet vectors of Mannheim curve pair in three-dimensional Euclidean space in terms of spinors has been investigated. In addition, the relations between spinors corresponding to Mannheim curve and Mannheim partner curve have been given by theorems. Moreover, geometric interpretations of spinors corresponding to Mannheim curve pair have been given. Then, the Mannheim curve has been considered as a helix and the spinor formulation in this case has been investigated. Finally, one example has been given. The fifth chapter consists of results and recommendations. Keywords: Euclidean Space, Mannheim Curve Pair, Spinors