Geometric visualization of evolved ruled surfaces via alternative frame in Lorentz-Minkowski 3-space

Yanlin Li; H. S. Abdel-Aziz; H. M. Serry; F. M. El-Adawy; M. Khalifa Saad; Yanlin Li; H. S. Abdel-Aziz; H. M. Serry; F. M. El-Adawy; M. Khalifa Saad

doi:10.3934/math.20241251

AIMS Mathematics

2024, Volume 9, Issue 9: 25619-25635. doi: 10.3934/math.20241251

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Geometric visualization of evolved ruled surfaces via alternative frame in Lorentz-Minkowski 3-space

1.
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
2.
Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt
3.
Mathematics Department, Faculty of Science, Suez Canal University, Ismailia, Egypt
4.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, KSA

Received: 06 May 2024 Revised: 09 August 2024 Accepted: 24 August 2024 Published: 03 September 2024
MSC : 53A04, 53A05

The main goal of this paper is to investigate the evolution equations for special types of timelike ruled surfaces with significant geometric and physical applications in Lorentz-Minkowski 3-space $ E_{1}^{3} $. Using the alternative frame associated with the basic curve of these surfaces, we explored their key geometric properties. Our analysis provided insights into the dynamics of local curvatures during their evolutions, enhancing the understanding of surface behavior. Finally, we present applications of our preliminary findings that contribute to the broader field of differential geometry.
- alternative frame,
- evolution of curves,
- evolution of surfaces,
- Lorentz-Minkowski 3-space
Citation: Yanlin Li, H. S. Abdel-Aziz, H. M. Serry, F. M. El-Adawy, M. Khalifa Saad. Geometric visualization of evolved ruled surfaces via alternative frame in Lorentz-Minkowski 3-space[J]. AIMS Mathematics, 2024, 9(9): 25619-25635. doi: 10.3934/math.20241251

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Abstract

The main goal of this paper is to investigate the evolution equations for special types of timelike ruled surfaces with significant geometric and physical applications in Lorentz-Minkowski 3-space $ E_{1}^{3} $. Using the alternative frame associated with the basic curve of these surfaces, we explored their key geometric properties. Our analysis provided insights into the dynamics of local curvatures during their evolutions, enhancing the understanding of surface behavior. Finally, we present applications of our preliminary findings that contribute to the broader field of differential geometry.

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