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10.3390/sym14040673
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Article

On the Bertrand Offsets of Timelike Ruled Surfaces in Minkowski 3-Space

by
Nadia Alluhaibi
1,*,†,
Rashad A. Abdel-Baky
2,† and
Monia Naghi
3,†
1
Department of Mathematics, Science and Arts College, King Abdulaziz University, Rabigh 25731, Saudi Arabia
2
Department of Mathematics, Faculty of Science, University of Assiut, Assiut 71516, Egypt
3
Department of Mathematics, Faculty of Science, King AbdulAziz University, Jeddah 22233, Saudi Arabia
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Symmetry 2022, 14(4), 673; https://doi.org/10.3390/sym14040673
Submission received: 27 February 2022 / Revised: 19 March 2022 / Accepted: 24 March 2022 / Published: 24 March 2022
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology)
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Abstract

This work examines some classical results of Bertrand curves for timelike ruled and developable surfaces using the E. Study map. This provides the ability to define two timelike ruled surfaces which are offset in the sense of Bertrand. It is shown that every timelike ruled surface has a Bertrand offset if and only if an equation should be satisfied between the dual geodesic curvatures. Some new results and theorems related to the developability of the Bertrand offsets of timelike ruled surfaces are also obtained.
Keywords: dual angle of pitch; Bertrand offsets; binormal surface dual angle of pitch; Bertrand offsets; binormal surface

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MDPI and ACS Style

Alluhaibi, N.; Abdel-Baky, R.A.; Naghi, M. On the Bertrand Offsets of Timelike Ruled Surfaces in Minkowski 3-Space. Symmetry 2022, 14, 673. https://doi.org/10.3390/sym14040673

AMA Style

Alluhaibi N, Abdel-Baky RA, Naghi M. On the Bertrand Offsets of Timelike Ruled Surfaces in Minkowski 3-Space. Symmetry. 2022; 14(4):673. https://doi.org/10.3390/sym14040673

Chicago/Turabian Style

Alluhaibi, Nadia, Rashad A. Abdel-Baky, and Monia Naghi. 2022. "On the Bertrand Offsets of Timelike Ruled Surfaces in Minkowski 3-Space" Symmetry 14, no. 4: 673. https://doi.org/10.3390/sym14040673

APA Style

Alluhaibi, N., Abdel-Baky, R. A., & Naghi, M. (2022). On the Bertrand Offsets of Timelike Ruled Surfaces in Minkowski 3-Space. Symmetry, 14(4), 673. https://doi.org/10.3390/sym14040673

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