New Version of Bäcklund Transformations for a Curve and Its Parallel Curve
In this paper, we study Bäcklund transformations for parallel curve given a space curve in the Euclidean 3-space. Firstly, we obtain Bishop frame on a parallel curve in E3. Then, it is obtained some essential equations of Bäcklund transformation with the aid of different characterizations of this frame. After this, we give a new theorem, Bäcklund transformations for the parallel curve according to Bishop frame in Euclidean 3-space. Finally, we compare with the main theorem of the results of Bäcklund transformations obtained for a curve and its parallel curve in E3.
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Document Type: Research Article
Publication date: September 1, 2018
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