New Version of Backlund Transformations for a Curve and Its Parallel Curve

Abstract

In this paper, we study Backlund transformations for parallel curve given a space curve in the Euclidean 3-space. Firstly, we obtain Bishop frame on a parallel curve in E-3. Then, it is obtained some essential equations of Backlund transformation with the aid of different characterizations of this frame. After this, we give a new theorem, Backlund transformations for the parallel curve according to Bishop frame in Euclidean 3-space. Finally, we compare with the main theorem of the results of Backlund transformations obtained for a curve and its parallel curve in E-3.