2020/08/13 by Mahmut Mak, Mak, Mahmut
Mathematics · Physics and Astronomy · #22E15 #53A04 #53A35 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications #math.DG #msc:22E15 #msc:53A04 #msc:53A35
paper · pdf · doi:10.48550/arxiv.2008.05831
16 pages
arxiv created 2020/08/13 · openalex publication_date 2020/08/13 · arxiv updated 2020/08/14 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this study, we introduce the natural mate and conjugate mate of a Frenet curve in a three dimensional Lie group \mathbbG with bi-invariant metric. Also, we give some relationships between a Frenet curve and its natural mate or its conjugate mate in \mathbbG . Especially, we obtain some results for the natural mate and the conjugate mate of a Frenet curve in \mathbbG 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.