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Journals / Fundamental Journal of Mathematics and Applications / 2026 / Volume: 5 Issue: 3

Generalized Bertrand and Mannheim Curves in 3D Lie Groups

Osman Zeki Okuyucu(BILECIK SEYH EDEBALI UNIVERSITY)0000-0003-4379-0252
Bahar Doğan Yazıcı(BILECIK SEYH EDEBALI UNIVERSITY)0000-0001-5690-4840
Pages
—
Publication Date
2022-09-23
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we give a new approach for Bertrand and Mannheim curves in $3D$ Lie groups with bi-invariant metrics.
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Key Findings & Data:In this paper, we give a new approach for Bertrand and Mannheim curves in $3D$ Lie groups with bi-invariant metrics.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Generalized Bertrand curves · Generalized Mannheim curves · Helix

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.

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Cite This Article

Okuyucu, O. Z., Yazıcı, B. D. (2022). Generalized Bertrand and Mannheim Curves in 3D Lie Groups. Fundamental Journal of Mathematics and Applications, Volume: 5 Issue: 3. https://doi.org/10.33401/fujma.1127839

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