Abstract

In this paper, we study Backlund transformations for the pedal curve given a space curve in the Euclidean 3-space. Firstly, we give Bishop frame on a pedal curve in $$ {\mathtt{E}}^{3} $$ . Then, we obtain some essential equations of Backlund transformation with the aid of different characterizations. Moreover, we give a main theorem, Backlund transformations for the pedal curve in Euclidean 3-space. Finally, it is obtained some results of Backlund transformations obtained for a pedal curve in $$ {\mathtt{E}}^{3} $$ .

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