Spacelike ruled surfaces with stationary Disteli-axis

Fatemah Mofarreh; Rashad A. Abdel-Baky; Fatemah Mofarreh; Rashad A. Abdel-Baky

doi:10.3934/math.2023394

AIMS Mathematics

2023, Volume 8, Issue 4: 7840-7855. doi: 10.3934/math.2023394

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Spacelike ruled surfaces with stationary Disteli-axis

Fatemah Mofarreh ¹,
Rashad A. Abdel-Baky ^{2
,
,}

1.
Mathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546 Saudi Arabia
2.
Department of Mathematics, Faculty of Science, University of Assiut, 71516 Assiut, Egypt

Received: 15 October 2022 Revised: 19 December 2022 Accepted: 09 January 2023 Published: 31 January 2023
MSC : 53A04, 53A05, 53A17

This paper derives the expressions for spacelike ruled surfaces with stationary Disteli-axis by means of the E. Study map. This provides the ability to compute a set of Lorentzian curvature functions which define the local shape of spacelike ruled surfaces. Consequently, some well-known formulae of surface theory at Lorentzian line space and their geometrical explanations are obtained and examined. Lastly, a characterization for a spacelike line trajectory to be a constant Disteli-axis is derived and investigated in detail.
- Disteli-axis,
- Serret-Frenet motion,
- striction curve
Citation: Fatemah Mofarreh, Rashad A. Abdel-Baky. Spacelike ruled surfaces with stationary Disteli-axis[J]. AIMS Mathematics, 2023, 8(4): 7840-7855. doi: 10.3934/math.2023394

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Abstract

This paper derives the expressions for spacelike ruled surfaces with stationary Disteli-axis by means of the E. Study map. This provides the ability to compute a set of Lorentzian curvature functions which define the local shape of spacelike ruled surfaces. Consequently, some well-known formulae of surface theory at Lorentzian line space and their geometrical explanations are obtained and examined. Lastly, a characterization for a spacelike line trajectory to be a constant Disteli-axis is derived and investigated in detail.

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