New approach to Bäcklund transformations for a curve and its pedal curve

Abstract

In this paper, we study Bäcklund transformations for the pedal curve given a space curve in the Euclidean 3-space. Firstly, we give Bishop frame on a pedal curve in E 3 . Then, we obtain some essential equations of Bäcklund transformation with the aid of different characterizations. Moreover, we give a main theorem, Bäcklund transformations for the pedal curve in Euclidean 3-space. Finally, it is obtained some results of Bäcklund transformations obtained for a pedal curve in E 3 . © 2018, African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature.