A natural Frenet frame for null curves on the lightlike cone in Minkowski space R 2 4 $\mathbb{R} ^{4}_{2}$
Abstract In this paper, we investigate the representation of curves on the lightlike cone Q 2 3 $\mathbb {Q}^{3}_{2}$ in Minkowski space R 2 4 $\mathbb {R}^{4}_{2}$ by structure functions. In addition, with this representation, we classify all of the null curves on the lightlike cone Q 2 3 $\mathbb...
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2020-10-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://link.springer.com/article/10.1186/s13660-020-02500-y |
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doaj-2bfcbdaacdbc4bcf85e1c73cbfc8d7b62020-11-25T04:00:26ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-10-012020111810.1186/s13660-020-02500-yA natural Frenet frame for null curves on the lightlike cone in Minkowski space R 2 4 $\mathbb{R} ^{4}_{2}$Nemat Abazari0Martin Bohner1Ilgin Sağer2Alireza Sedaghatdoost3Yusuf Yayli4Department of Mathematics and Applications, University of Mohaghegh ArdabiliDepartment of Mathematics and Statistics, Missouri S&TDepartment of Mathematics and Computer Science, University of Missouri—St. LouisDepartment of Mathematics and Applications, University of Mohaghegh ArdabiliDepartment of Mathematics, Faculty of Science, Ankara UniversityAbstract In this paper, we investigate the representation of curves on the lightlike cone Q 2 3 $\mathbb {Q}^{3}_{2}$ in Minkowski space R 2 4 $\mathbb {R}^{4}_{2}$ by structure functions. In addition, with this representation, we classify all of the null curves on the lightlike cone Q 2 3 $\mathbb {Q}^{3}_{2}$ 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 κ 2 = 0 $\kappa _{2}=0$ , and we show that any null curve on the lightlike cone is a helix. Finally, we find all curves with constant curvature functions.http://link.springer.com/article/10.1186/s13660-020-02500-yConstant curvature functionHelixLightlike coneNatural Frenet frameNull curve |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Nemat Abazari Martin Bohner Ilgin Sağer Alireza Sedaghatdoost Yusuf Yayli |
| spellingShingle |
Nemat Abazari Martin Bohner Ilgin Sağer Alireza Sedaghatdoost Yusuf Yayli A natural Frenet frame for null curves on the lightlike cone in Minkowski space R 2 4 $\mathbb{R} ^{4}_{2}$ Journal of Inequalities and Applications Constant curvature function Helix Lightlike cone Natural Frenet frame Null curve |
| author_facet |
Nemat Abazari Martin Bohner Ilgin Sağer Alireza Sedaghatdoost Yusuf Yayli |
| author_sort |
Nemat Abazari |
| title |
A natural Frenet frame for null curves on the lightlike cone in Minkowski space R 2 4 $\mathbb{R} ^{4}_{2}$ |
| title_short |
A natural Frenet frame for null curves on the lightlike cone in Minkowski space R 2 4 $\mathbb{R} ^{4}_{2}$ |
| title_full |
A natural Frenet frame for null curves on the lightlike cone in Minkowski space R 2 4 $\mathbb{R} ^{4}_{2}$ |
| title_fullStr |
A natural Frenet frame for null curves on the lightlike cone in Minkowski space R 2 4 $\mathbb{R} ^{4}_{2}$ |
| title_full_unstemmed |
A natural Frenet frame for null curves on the lightlike cone in Minkowski space R 2 4 $\mathbb{R} ^{4}_{2}$ |
| title_sort |
natural frenet frame for null curves on the lightlike cone in minkowski space r 2 4 $\mathbb{r} ^{4}_{2}$ |
| publisher |
SpringerOpen |
| series |
Journal of Inequalities and Applications |
| issn |
1029-242X |
| publishDate |
2020-10-01 |
| description |
Abstract In this paper, we investigate the representation of curves on the lightlike cone Q 2 3 $\mathbb {Q}^{3}_{2}$ in Minkowski space R 2 4 $\mathbb {R}^{4}_{2}$ by structure functions. In addition, with this representation, we classify all of the null curves on the lightlike cone Q 2 3 $\mathbb {Q}^{3}_{2}$ 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 κ 2 = 0 $\kappa _{2}=0$ , and we show that any null curve on the lightlike cone is a helix. Finally, we find all curves with constant curvature functions. |
| topic |
Constant curvature function Helix Lightlike cone Natural Frenet frame Null curve |
| url |
http://link.springer.com/article/10.1186/s13660-020-02500-y |
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