当前位置: X-MOL 学术J. Inequal. Appl. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A natural Frenet frame for null curves on the lightlike cone in Minkowski space \(\mathbb{R} ^{4}_{2}\)
Journal of Inequalities and Applications ( IF 1.5 ) Pub Date : 2020-10-29 , DOI: 10.1186/s13660-020-02500-y
Nemat Abazari , Martin Bohner , Ilgin Sağer , Alireza Sedaghatdoost , Yusuf Yayli

In this paper, we investigate the representation of curves on the lightlike cone $\mathbb {Q}^{3}_{2}$ in Minkowski space $\mathbb {R}^{4}_{2}$ by structure functions. In addition, with this representation, we classify all of the null curves on the lightlike cone $\mathbb {Q}^{3}_{2}$ in four types, and we obtain a natural Frenet frame for these null curves. Furthermore, for this natural Frenet frame, we calculate curvature functions of a null curve, especially the curvature function $\kappa _{2}=0$ , and we show that any null curve on the lightlike cone is a helix. Finally, we find all curves with constant curvature functions.

中文翻译:

Minkowski空间\(\ mathbb {R} ^ {4} _ {2} \)中光锥上的空曲线的自然Frenet框架

在本文中,我们通过结构函数研究了Minkowski空间$ \ mathbb {R} ^ {4} _ {2} $中的光锥$ \ mathbb {Q} ^ {3} _ {2} $上曲线的表示形式。另外,通过这种表示,我们将光锥$ \ mathbb {Q} ^ {3} _ {2} $上的所有空曲线分为四种类型,并为这些空曲线获得自然的Frenet帧。此外,对于此自然Frenet帧,我们计算零曲线的曲率函数,尤其是曲率函数$ \ kappa _ {2} = 0 $,并且我们证明,光锥上的任何零曲线都是螺旋。最后,我们找到所有具有恒定曲率函数的曲线。
更新日期:2020-10-30
down
wechat
bug