Mathematics and Statistics Vol. 10(4), pp. 884 - 893
DOI: 10.13189/ms.2022.100420
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Evolution Equations of Pseudo Spherical Images for Timelike Curves in Minkowski 3-Space

H. S. Abdel-Aziz ¹, H. Serry ², M. Khalifa Saad ^1,3,*
1 Department of Mathematics, Faculty of Science, Sohag University, 82524 Sohag, EGYPT
² Department of Mathematics, Faculty of Science, Suez Canal University, Ismailia, EGYPT
³ Department of Mathematics, Faculty of Science, Islamic University of Madinah, 170 Al-Madinah, KSA

ABSTRACT

The pseudo spherical images of non-lightlike curves in Minkowski geometry are curves on the unit pseudo sphere, which are intimately related to the curvatures of the original ones. These images are obtained by means of Frenet-Serret frame vector fields associated with the curves. This classical topic is a well-known concept in Lorentzian geometry of curves. In this paper, we introduce the pseudo spherical images for a timelike curve in Minkowski 3-space. Our main purpose of the work is to obtain the time evolution equations of the orthonormal frame and curvatures of these images. The compatibility conditions for the evolutions are used. Finally, the theoretical results obtained through this study are given by some important theorems and explained in two computational examples with the corresponding graphs.

KEYWORDS
Evolution Equations, Timelike Curves, Pseudo Spherical Images, Serret-Frenet Frame

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] H. S. Abdel-Aziz , H. Serry , M. Khalifa Saad , "Evolution Equations of Pseudo Spherical Images for Timelike Curves in Minkowski 3-Space," Mathematics and Statistics, Vol. 10, No. 4, pp. 884 - 893, 2022. DOI: 10.13189/ms.2022.100420.

(b). APA Format:
H. S. Abdel-Aziz , H. Serry , M. Khalifa Saad (2022). Evolution Equations of Pseudo Spherical Images for Timelike Curves in Minkowski 3-Space. Mathematics and Statistics, 10(4), 884 - 893. DOI: 10.13189/ms.2022.100420.