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

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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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Keywords: BISHOP FRAME; BÄCKLUND TRANSFORMATIONS; PARALLEL CURVE

Document Type: Research Article

Publication date: September 1, 2018

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  • Journal of Advanced Physics is an interdisciplinary peer-reviewed journal consolidating research activities in all experimental and theoretical aspects of advanced physics. The journal aims in publishing articles of novel and frontier physics that merit the attention and interest of the whole physics community. JAP publishes review articles, full research articles, short communications of important new scientific and technological findings in all latest research aspects of physics.
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