Spinor Equations of Successor Curves

The aim of this study is to give spinor representation of successor curves in three-dimensional Euclidean space. In this study, the spinor representations of a curve with arc-length parameter and a successor curve of this curve with some arc-length parameter in three dimensional Euclidean space have been studied. For this, first of all, the curve with unit speed and its successor curve have been corresponded to two different spinors. Then, using the relationships between these curves, the relationships between the spinors corresponding to these curves have been given. Therefore, geometric interpretations of these curves and corresponding spinors have been made. In addition, different spinor equations of the mates and derivatives of these spinors have been examined and geometric interpretations of these spinor equations have been given. Then, spinor equations have been obtained in case the successor curves are helices. Consequently, two examples have been given. © 2022, Emrah Evren KARA. All rights reserved.