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Symmetry
Volume 14
Issue 4
10.3390/sym14040716
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Article

Singularities of Non-Developable Ruled Surface with Space-like Ruling

by
Rashad Abdel-Satar Abdel-Baky
1,† and
Mohamed Khalifa Saad
2,3,*,†
1
Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt
2
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
3
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina 42351, Saudi Arabia
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Symmetry 2022, 14(4), 716; https://doi.org/10.3390/sym14040716
Submission received: 1 March 2022 / Revised: 11 March 2022 / Accepted: 21 March 2022 / Published: 1 April 2022
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology)
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Abstract

Singularity theory is a significant field of modern mathematical research. The main goal in most problems of singularity theory is to understand the dependence of some objects in analysis and geometry, or physics; or from some other science on parameters. In this paper, we study the singularities of the spherical indicatrix and evolute of space-like ruled surface with space-like ruling. The main method takes advantage of the classical unfolding theorem in singularity theory, which is a classical method to study singularity problems in Euclidean space and Minkowski space. Finally, we provide an example to illustrate our results.
Keywords: Blaschke frame; evolute of the dual spherical curve; singularity Blaschke frame; evolute of the dual spherical curve; singularity

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MDPI and ACS Style

Abdel-Baky, R.A.-S.; Saad, M.K. Singularities of Non-Developable Ruled Surface with Space-like Ruling. Symmetry 2022, 14, 716. https://doi.org/10.3390/sym14040716

AMA Style

Abdel-Baky RA-S, Saad MK. Singularities of Non-Developable Ruled Surface with Space-like Ruling. Symmetry. 2022; 14(4):716. https://doi.org/10.3390/sym14040716

Chicago/Turabian Style

Abdel-Baky, Rashad Abdel-Satar, and Mohamed Khalifa Saad. 2022. "Singularities of Non-Developable Ruled Surface with Space-like Ruling" Symmetry 14, no. 4: 716. https://doi.org/10.3390/sym14040716

APA Style

Abdel-Baky, R. A.-S., & Saad, M. K. (2022). Singularities of Non-Developable Ruled Surface with Space-like Ruling. Symmetry, 14(4), 716. https://doi.org/10.3390/sym14040716

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