论文标题
三维谎言组的Frenet曲线的自然和共轭伴侣
Natural and Conjugate Mates of Frenet Curves in Three-Dimensional Lie Group
论文作者
论文摘要
在这项研究中，我们以双维式$ \ mathbb {g} $中的双层式指标介绍了Frenet曲线的自然伴侣和偶联伴侣。另外，我们在$ \ mathbb {g} $中提供了Frenet曲线及其自然伴侣或其偶联伴侣之间的一些关系。特别是，当Frenet曲线是一般螺旋，倾斜螺旋，球形曲线，一个旋转曲线，salkowski（salkowski and salkowski and anstant curvature and nort-clastant and-clonstki and-antski）时Bertrand曲线。最后，我们在Euclidean 3空间中使用数字解决方案提供了不错的图形，作为交换性谎言组。
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.
