New approach to Bäcklund transformations for a curve and its pedal curve. (English) Zbl 1438.53012
Summary: 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 \( {\mathtt{E}}^{3} \). 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 \( {\mathtt{E}}^{3} \).
MSC:
| 53A04 | Curves in Euclidean and related spaces |
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