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Research Article | Open Access

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

Yanlin Li1, Ali. H. Alkhaldi2, Akram Ali2( ), R. A. Abdel-Baky3, M. Khalifa Saad4,5
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Department of Mathematics, College of Science, King Khalid University, Abha 61413, KSA
Department of Mathematics, Faculty of Science, Assiut University, 71516 Assiut, Egypt
Department of Mathematics, Faculty of Science, Islamic University of Madinah, KSA
Department of Mathematics, Faculty of Science, Sohag University, 82524 Sohag, Egypt
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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.

Keywords

Blaschke framegeodesic curvaturesingularity theoryspherical indicatrixruled surfaces
CLC number: 53A04, 53A05, 53A17

References

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AIMS Mathematics
Volume 8 Issue 6,
June 2023
Pages 13875-13888
DOI: 10.3934/math.2023709

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Cite this article:
Li Y, Alkhaldi AH, Ali A, et al. Investigation of ruled surfaces and their singularities according to Blaschke frame in Euclidean 3-space. AIMS Mathematics, 2023, 8(6): 13875-13888. https://doi.org/10.3934/math.2023709

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Received: 10 February 2023
Revised: 24 March 2023
Accepted: 30 March 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)