Investigation of ruled surfaces and their singularities according to Blaschke frame in Euclidean $ 3 $-space

Yanlin Li; Ali. H. Alkhaldi; Akram Ali; R. A. Abdel-Baky; M. Khalifa Saad; Yanlin Li; Ali. H. Alkhaldi; Akram Ali; R. A. Abdel-Baky; M. Khalifa Saad

doi:10.3934/math.2023709

AIMS Mathematics

2023, Volume 8, Issue 6: 13875-13888. doi: 10.3934/math.2023709

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Investigation of ruled surfaces and their singularities according to Blaschke frame in Euclidean $ 3 $-space

1.
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
2.
Department of Mathematics, College of Science, King Khalid University, Abha 61413, KSA
3.
Department of Mathematics, Faculty of Science, Assiut University, 71516 Assiut, Egypt
4.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, KSA
5.
Department of Mathematics, Faculty of Science, Sohag University, 82524 Sohag, Egypt

Received: 10 February 2023 Revised: 24 March 2023 Accepted: 30 March 2023 Published: 12 April 2023
MSC : 53A04, 53A05, 53A17

In this paper, we study the singularities on a non-developable ruled surface according to Blaschke's frame in the Euclidean 3-space. Additionally, we prove that singular points occur on this kind of ruled surface and use the singularity theory technique to examine these singularities. Finally, we construct an example to confirm and demonstrate our primary finding.
- Blaschke frame,
- geodesic curvature,
- singularity theory,
- spherical indicatrix,
- ruled surfaces
Citation: Yanlin Li, Ali. H. Alkhaldi, Akram Ali, R. A. Abdel-Baky, M. Khalifa Saad. Investigation of ruled surfaces and their singularities according to Blaschke frame in Euclidean $ 3 $-space[J]. AIMS Mathematics, 2023, 8(6): 13875-13888. doi: 10.3934/math.2023709

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Abstract

In this paper, we study the singularities on a non-developable ruled surface according to Blaschke's frame in the Euclidean 3-space. Additionally, we prove that singular points occur on this kind of ruled surface and use the singularity theory technique to examine these singularities. Finally, we construct an example to confirm and demonstrate our primary finding.

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