Mathematics and Statistics Vol. 8(3), pp. 299 - 305
DOI: 10.13189/ms.2020.080308
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Characterizations of Some Special Curves in Lorentz-Minkowski Space

M. Khalifa Saad ^1,2,*, R. A. Abdel-Baky ^3,4, F. Alharbi ¹, A. Aloufi ^1
1 Department of Mathematics, Faculty of Science, Islamic University of Madinah, 170 Al-Madinah, KSA
² Department of Mathematics, Faculty of Science, Sohag University, 82524 Sohag, Egypt
³ Department of Mathematics, Sciences Faculty for Girls, Jeddah University, 21352 Jeddah, KSA
⁴ Department of Mathematics, Faculty of Science, Assiut University, 71516 Assiut, Egypt

ABSTRACT

In a theory of space curves, especially, a helix is the most elementary and interesting topic. A helix, moreover, pays attention to natural scientists as well as mathematicians because of its various applications, for example, DNA, carbon nanotube, screws, springs and so on. Also there are many applications of helix curve or helical structures in Science such as fractal geometry, in the fields of computer aided design and computer graphics. Helices can be used for the tool path description, the simulation of kinematic motion or the design of highways, etc. The problem of the determination of parametric representation of the position vector of an arbitrary space curve according to the intrinsic equations is still open in the Euclidean space E³ and in the Minkowski space . In this paper, we introduce some characterizations of a non-null slant helix which has a spacelike or timelike axis in . We use vector differential equations established by means of Frenet equations in Minkowski space . Also, we investigate some differential geometric properties of these curves according to these vector differential equations. Besides, we illustrate some examples to confirm our findings.

KEYWORDS
Frenet Formulae, Spacelike Curve, Timelike Curve, Position Vector, Slant Helix

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] M. Khalifa Saad , R. A. Abdel-Baky , F. Alharbi , A. Aloufi , "Characterizations of Some Special Curves in Lorentz-Minkowski Space," Mathematics and Statistics, Vol. 8, No. 3, pp. 299 - 305, 2020. DOI: 10.13189/ms.2020.080308.

(b). APA Format:
M. Khalifa Saad , R. A. Abdel-Baky , F. Alharbi , A. Aloufi (2020). Characterizations of Some Special Curves in Lorentz-Minkowski Space. Mathematics and Statistics, 8(3), 299 - 305. DOI: 10.13189/ms.2020.080308.