Affiliation:
1. BİLECİK ŞEYH EDEBALİ ÜNİVERSİTESİ
2. SAKARYA ÜNİVERSİTESİ
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.
Publisher
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
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https://doi.org/10.1007/s00229-003-0357-5