The Spinor Expressions of Mannheim Curves in Euclidean 3-Space

In this paper, the spinor formulations of Mannheim curve pair are investigated. First of all, two spinors corresponding to Mannheim curve pair are given and considering the relationships between the Frenet frames of Mannheim curve pair the relationship between two spinors corresponding to this curve pair are obtained. Therefore, some geometric interpretations of spinors are obtained using the Mannheim curve pair and considering Mannheim curve as helix the spinor formulations of Mannheim curve pair are given. Moreover, the spinor formulations for the curvatures of the Mannheim curve pair are also obtained. Consequently, an example of these spinors is given. Therefore, it is thought that this study will make an important contribution to the mathematical analysis and geometric interpretation of spinors, which have many uses in physics.