Vector fields on bifurcation diagrams of quasi singularities
We describe the generators of the vector fields tangent to the bifurcation diagrams and caustics of simple quasi boundary singularities. As an application, submersions on the pair $ (G, B) $, which consists of a cuspidal edge $ G $ in $ \mathbb{R}^3 $ that contains a distinguishing regular curve $ B...
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241710 |
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| author | Fawaz Alharbi Yanlin Li |
| author_facet | Fawaz Alharbi Yanlin Li |
| author_sort | Fawaz Alharbi |
| collection | DOAJ |
| description | We describe the generators of the vector fields tangent to the bifurcation diagrams and caustics of simple quasi boundary singularities. As an application, submersions on the pair $ (G, B) $, which consists of a cuspidal edge $ G $ in $ \mathbb{R}^3 $ that contains a distinguishing regular curve $ B $, are classified. This classification was used as a means to investigate the contact that a general cuspidal edge $ G $ equipped with a regular curve $ B\subset G $ has with planes. The singularities of the height functions on $ (G, B) $ are discussed and they are related to the curvatures and torsions of the distinguished curves on the cuspidal edge. In addition to this, the discriminants of the versal deformations of the submersions that were accomplished are described and they are related to the duality of the cuspidal edge. |
| format | Article |
| id | doaj-art-69e88e9a333b4e76aad3ef4048633311 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-69e88e9a333b4e76aad3ef40486333112025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912360473606810.3934/math.20241710Vector fields on bifurcation diagrams of quasi singularitiesFawaz Alharbi0Yanlin Li1Department of Mathematics, College of Sciences, Umm Al-Qura University, Makkah 21955, Saudi ArabiaSchool of Mathematics, Hangzhou Normal University, Hangzhou 311121, ChinaWe describe the generators of the vector fields tangent to the bifurcation diagrams and caustics of simple quasi boundary singularities. As an application, submersions on the pair $ (G, B) $, which consists of a cuspidal edge $ G $ in $ \mathbb{R}^3 $ that contains a distinguishing regular curve $ B $, are classified. This classification was used as a means to investigate the contact that a general cuspidal edge $ G $ equipped with a regular curve $ B\subset G $ has with planes. The singularities of the height functions on $ (G, B) $ are discussed and they are related to the curvatures and torsions of the distinguished curves on the cuspidal edge. In addition to this, the discriminants of the versal deformations of the submersions that were accomplished are described and they are related to the duality of the cuspidal edge.https://www.aimspress.com/article/doi/10.3934/math.20241710bifurcation diagramcausticvector fieldcuspidal edgecontactcurvatures and torsionsheight functioncontactdeformationsdiscriminatdaul |
| spellingShingle | Fawaz Alharbi Yanlin Li Vector fields on bifurcation diagrams of quasi singularities AIMS Mathematics bifurcation diagram caustic vector field cuspidal edge contact curvatures and torsions height function contact deformations discriminat daul |
| title | Vector fields on bifurcation diagrams of quasi singularities |
| title_full | Vector fields on bifurcation diagrams of quasi singularities |
| title_fullStr | Vector fields on bifurcation diagrams of quasi singularities |
| title_full_unstemmed | Vector fields on bifurcation diagrams of quasi singularities |
| title_short | Vector fields on bifurcation diagrams of quasi singularities |
| title_sort | vector fields on bifurcation diagrams of quasi singularities |
| topic | bifurcation diagram caustic vector field cuspidal edge contact curvatures and torsions height function contact deformations discriminat daul |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241710 |
| work_keys_str_mv | AT fawazalharbi vectorfieldsonbifurcationdiagramsofquasisingularities AT yanlinli vectorfieldsonbifurcationdiagramsofquasisingularities |