Sweeping surfaces generated by involutes of a spacelike curve with a timelike binormal in Minkowski 3-space

Özgür Boyacıoğlu Kalkan; Süleyman Şenyurt; Mustafa Bilici; Davut Canlı; Özgür Boyacıoğlu Kalkan; Süleyman Şenyurt; Mustafa Bilici; Davut Canlı

doi:10.3934/math.2025047

AIMS Mathematics

2025, Volume 10, Issue 1: 988-1007. doi: 10.3934/math.2025047

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Research article

Sweeping surfaces generated by involutes of a spacelike curve with a timelike binormal in Minkowski 3-space

1.
Afyon Vocational School, Afyon Kocatepe University, Afyonkarahisar, 03200, Türkiye
2.
Department of Mathematics, Ordu University, Ordu, 52200, Türkiye
3.
Department of Mathematics, Ondokuz Mayıs University, Samsun, 55270, Türkiye

Received: 14 November 2024 Revised: 02 January 2025 Accepted: 07 January 2025 Published: 16 January 2025
MSC : 53A04, 53A05

In this paper, we studied the geometry of sweeping surfaces generated by the involutes of spacelike curves with a timelike binormal in Minkowski 3-space $ E_1^3 $. First, we investigated the singularity concept, and the mean and Gaussian curvatures of these surfaces. Then, we provided the requirements for the surface to be developable (flat) and minimal. We also determined the sufficient and necessary conditions for the parameter curves of these surfaces to be geodesic and asymptotic. Moreover, we analyzed these surfaces when the parameter curves are lines of curvature on the surface. Finally, the examples of these surfaces were given and their corresponding figures were drawn.
- sweeping surface,
- involute curve,
- Minkowski space,
- developable and minimal surface,
- geodesic curve,
- asymptotic curve
Citation: Özgür Boyacıoğlu Kalkan, Süleyman Şenyurt, Mustafa Bilici, Davut Canlı. Sweeping surfaces generated by involutes of a spacelike curve with a timelike binormal in Minkowski 3-space[J]. AIMS Mathematics, 2025, 10(1): 988-1007. doi: 10.3934/math.2025047

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Abstract

In this paper, we studied the geometry of sweeping surfaces generated by the involutes of spacelike curves with a timelike binormal in Minkowski 3-space $ E_1^3 $. First, we investigated the singularity concept, and the mean and Gaussian curvatures of these surfaces. Then, we provided the requirements for the surface to be developable (flat) and minimal. We also determined the sufficient and necessary conditions for the parameter curves of these surfaces to be geodesic and asymptotic. Moreover, we analyzed these surfaces when the parameter curves are lines of curvature on the surface. Finally, the examples of these surfaces were given and their corresponding figures were drawn.

References

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