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

Authors : Mahmut MAK

Pages : 522-540

Doi:10.31801/cfsuasmas.785489

View : 17 | Download : 12

Publication Date : 2021-06-30

Article Type : Research Paper

Abstract :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 insert ignore into journalissuearticles values(constant curvature and non-constant torsion);, anti-Salkowski insert ignore into journalissuearticles values(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.
Keywords : Natural mate, conjugate mate, helix, slant helix, spherical curve, rectifying curve, Salkowski curve, anti Salkowski curve