On admissible curves and their evolution equations in pseudo-Galilean space

Volume 25, Issue 4, pp 370--380
Publication Date: August 12, 2021 Submission Date: June 18, 2021 Revision Date: July 08, 2021 Accteptance Date: July 11, 2021
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Authors

H. S. Abdel-Aziz - Department of Mathematics, Sohag University, Sohag 82524, Egypt. H. M. Serry - Department of Mathematics, Suez Canal University, Ismailia, Egypt. F. M. El-Adawy - Department of Mathematics, Suez Canal University, Ismailia, Egypt. A. A. Khalil - Department of Mathematics, Sohag University, Sohag 82524, Egypt.

Abstract

The evolution equations of some forms of admissible curves in the pseudo-Galilean Space $G_{3}^1$ are investigated in this paper. In more detail, we use two separate methods to obtain coupled nonlinear partial differential equations of time evolution in terms of their curvatures. The first method studies the evolution equations for admissible curves via the frame field, while the second studies the evolution equations via the velocity vector. Then, the position vectors of the evolving curves are formulated. Also, we conduct comparative research of the evolution equations for curves in different spaces. We furthermore present some models as an application of the evolution equations of the curvature and torsion for admissible curves, confirming our theoretical results.

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ISRP Style

H. S. Abdel-Aziz, H. M. Serry, F. M. El-Adawy, A. A. Khalil, On admissible curves and their evolution equations in pseudo-Galilean space, Journal of Mathematics and Computer Science, 25 (2022), no. 4, 370--380

AMA Style

Abdel-Aziz H. S., Serry H. M., El-Adawy F. M., Khalil A. A., On admissible curves and their evolution equations in pseudo-Galilean space. J Math Comput SCI-JM. (2022); 25(4):370--380

Chicago/Turabian Style

Abdel-Aziz, H. S., Serry, H. M., El-Adawy, F. M., Khalil, A. A.. "On admissible curves and their evolution equations in pseudo-Galilean space." Journal of Mathematics and Computer Science, 25, no. 4 (2022): 370--380

Keywords

• evolution equations
• Frenet frame
• pseudo-Galilean space
• spacelike and timelike curves

•  53A35

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