Generalized Bertrand and Mannheim Curves in 3D Lie Groups

Authors : Osman Zeki OKUYUCU, Bahar DOĞAN YAZICI

Pages : 201-209

Doi:10.33401/fujma.1127839

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Publication Date : 2022-09-23

Article Type : Research Paper

Abstract :In this paper, we give a new approach for Bertrand and Mannheim curves in $3D$ Lie groups with bi-invariant metrics. In this way, some conditions including the known results have been given for a curve to be Bertrand or Mannheim curve in $3D$ Euclidean space and in $3D$ Lie groups.
Keywords : Generalized Bertrand curves, Generalized Mannheim curves, Helix, Lie groups, Slant helix