In this study, we introduce the natural mate and conjugate mate of a Frenet curve in a three dimensional Lie group $ \mathbb{G} $ with bi-invariant metric. Also, we give some relationships between a Frenet curve and its natural mate or its conjugate mate in $ \mathbb{G} $. Especially, we obtain some results for the natural mate and the conjugate mate of a Frenet curve in $ \mathbb{G} $ when the Frenet curve is a general helix, a slant helix, a spherical curve, a rectifying curve, a Salkowski (constant curvature and non-constant torsion), anti-Salkowski (non-constant curvature and constant torsion), Bertrand curve. Finally, we give nice graphics with numeric solution in Euclidean 3-space as a commutative Lie group.
Natural mate conjugate mate helix slant helix spherical curve rectifying curve Salkowski curve anti-Salkowski curve
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Birincil Dil | İngilizce |
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Konular | Matematik |
Bölüm | Research Article |
Yazarlar | |
Proje Numarası | --- |
Yayımlanma Tarihi | 30 Haziran 2021 |
Gönderilme Tarihi | 25 Ağustos 2020 |
Kabul Tarihi | 1 Şubat 2021 |
Yayımlandığı Sayı | Yıl 2021 Cilt: 70 Sayı: 1 |
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
This work is licensed under a Creative Commons Attribution 4.0 International License.