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,...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-04-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023709?viewType=HTML |
| _version_ | 1827963731340951552 |
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| author | Yanlin Li Ali. H. Alkhaldi Akram Ali R. A. Abdel-Baky M. Khalifa Saad |
| author_facet | Yanlin Li Ali. H. Alkhaldi Akram Ali R. A. Abdel-Baky M. Khalifa Saad |
| author_sort | Yanlin Li |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T17:03:51Z |
| format | Article |
| id | doaj.art-19180220bf3444e5bdd4e153331a73d1 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-09T17:03:51Z |
| publishDate | 2023-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-19180220bf3444e5bdd4e153331a73d12023-04-21T01:20:30ZengAIMS PressAIMS Mathematics2473-69882023-04-0186138751388810.3934/math.2023709Investigation of ruled surfaces and their singularities according to Blaschke frame in Euclidean 3-spaceYanlin Li 0Ali. H. Alkhaldi1Akram Ali 2R. A. Abdel-Baky3M. Khalifa Saad 41. School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China2. Department of Mathematics, College of Science, King Khalid University, Abha 61413, KSA2. Department of Mathematics, College of Science, King Khalid University, Abha 61413, KSA3. Department of Mathematics, Faculty of Science, Assiut University, 71516 Assiut, Egypt4. Department of Mathematics, Faculty of Science, Islamic University of Madinah, KSA 5. Department of Mathematics, Faculty of Science, Sohag University, 82524 Sohag, EgyptIn 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.https://www.aimspress.com/article/doi/10.3934/math.2023709?viewType=HTMLblaschke framegeodesic curvaturesingularity theoryspherical indicatrixruled surfaces |
| spellingShingle | 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 AIMS Mathematics blaschke frame geodesic curvature singularity theory spherical indicatrix ruled surfaces |
| title | Investigation of ruled surfaces and their singularities according to Blaschke frame in Euclidean 3-space |
| title_full | Investigation of ruled surfaces and their singularities according to Blaschke frame in Euclidean 3-space |
| title_fullStr | Investigation of ruled surfaces and their singularities according to Blaschke frame in Euclidean 3-space |
| title_full_unstemmed | Investigation of ruled surfaces and their singularities according to Blaschke frame in Euclidean 3-space |
| title_short | Investigation of ruled surfaces and their singularities according to Blaschke frame in Euclidean 3-space |
| title_sort | investigation of ruled surfaces and their singularities according to blaschke frame in euclidean 3 space |
| topic | blaschke frame geodesic curvature singularity theory spherical indicatrix ruled surfaces |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023709?viewType=HTML |
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