On special singular curve couples of framed curves in 3D Lie groups

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume:72 Issue:3
On special singular curve couples of framed curves in 3D Lie groups

On special singular curve couples of framed curves in 3D Lie groups

Authors : Bahar DOĞAN YAZICI, Osman Zeki OKUYUCU, Murat TOSUN

Pages : 710-720

Doi:10.31801/cfsuasmas.1197154

View : 26 | Download : 40

Publication Date : 2023-09-30

Article Type : Research Paper

Abstract :In this paper, we introduce Bertrand and Mannheim curves of framed curves, which are a special singular curve in 3D Lie groups. We explain the conditions for framed curves to be Bertrand curves and Mannheim curves in 3D Lie groups. We give relationships between framed curvatures and Lie curvatures of Bertrand and Mannheim curves of framed curves. In addition, we obtain the characterization of Bertrand and Mannheim curves according to the various frames of framed curves in 3D Lie groups.
Keywords : Bertrand curves, Mannheim curves, framed curves, Lie groups

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