Generalized Bertrand and Mannheim Curves in 3D Lie Groups

Okuyucu, O. Zeki; Yazıcı, Bahar Doğan

doi:10.33401/fujma.1127839

Fundamental Journal of Mathematics and Applications

2022

DOI: 10.33401/fujma.1127839

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Generalized Bertrand and Mannheim Curves in 3D Lie Groups

O. Zeki Okuyucu

Bahar Doğan Yazıcı

Abstract: In this paper, we give a new approach for Bertrand and Mannheim curves in 3D Lie groups with bi-invariant metric. By the 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.

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Mannheim partner curves in the special linear group

Thiago¹

2023

Int. J. Phys. Sci.

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In this study, we state some basic results about the geometry of the special linear group SL(2,R), seen as a subset of , in terms of the left invariant fields, such as bracketing, Levi Civita connection ∇ and Riemann curvature tensor R, we give some basic theorems for Mannheim partner curves in the special linear group. We also find the relations between the curvatures and torsions of these associated curves and we give necessary and sufficient conditions for a given curve to be a Mannheim partner curve of another given curve through a relation between its curvature and torsion.

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Mannheim partner curves in the special linear group

Thiago¹

2023

Int. J. Phys. Sci.

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Generalized Bertrand and Mannheim Curves in 3D Lie Groups

Abstract: In this paper, we give a new approach for Bertrand and Mannheim curves in 3D Lie groups with bi-invariant metric. By the 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.

Cited by 1 publication

References 16 publications

Mannheim partner curves in the special linear group

Mannheim partner curves in the special linear group

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