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

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,...

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Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 6; pp. 13875 - 13888
Main Authors Li, Yanlin, Alkhaldi, Ali. H., Ali, Akram, Abdel-Baky, R. A., Saad, M. Khalifa
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
blaschke frame
geodesic curvature
ruled surfaces
singularity theory
spherical indicatrix
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2023709