Natural and conjugate mates of Frenet curves in three-dimensional Lie group

DOI10.31801/cfsuasmas.785489zbMath1495.53031arXiv2008.05831OpenAlexW3159596241WikidataQ115222916 ScholiaQ115222916MaRDI QIDQ5083571

Mahmut Mak

Publication date: 20 June 2022

Published in: Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.05831

zbMATH Keywords

helixslant helixrectifying curvespherical curveSalkowski curveanti-Salkowski curveconjugate matenatural mate

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) General properties and structure of real Lie groups (22E15) Local submanifolds (53B25) Curves in Euclidean and related spaces (53A04) Non-Euclidean differential geometry (53A35)

Cites Work

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• Associated curves of a Frenet curve and their applications
• Salkowski curves revisited: a family of curves with constant curvature and non-constant torsion
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• A generalization of Lancret's theorem
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• General helices of AW(k)-type in the Lie group
• Darboux helices in three dimensional Lie groups
• Associated Curves of Frenet curves in Three Dimensional Compact Lie Group
• When Does the Position Vector of a Space Curve Always Lie in Its Rectifying Plane?
• On Mannheim Partner Curves in three Dimensional Lie Groups
• Bertrand Curves in three Dimensional Lie Groups

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