Singularities of Osculating Developable Surfaces of Timelike Surfaces along Curves
In this paper, we focus on a developable surface tangent to a timelike surface along a curve in Minkowski 3-space, which is called the <i>osculating developable surface</i> of the timelike surface along the curve. The ruling of the osculating developable surface is parallel to the <i&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/11/2251 |
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| author | Yongqiao Wang Lin Yang Pengcheng Li Yuan Chang |
| author_facet | Yongqiao Wang Lin Yang Pengcheng Li Yuan Chang |
| author_sort | Yongqiao Wang |
| collection | DOAJ |
| description | In this paper, we focus on a developable surface tangent to a timelike surface along a curve in Minkowski 3-space, which is called the <i>osculating developable surface</i> of the timelike surface along the curve. The ruling of the osculating developable surface is parallel to the <i>osculating Darboux vector field</i>. The main goal of this paper is to classify the singularities of the osculating developable surface. To this end, two new invariants of curves are defined to characterize these singularities. Meanwhile, we also research the singular properties of osculating developable surfaces near their lightlike points. Moreover, we give a relation between osculating Darboux vector fields and normal vector fields of timelike surfaces along curves from the viewpoint of Legendrian dualities. Finally, some examples with symmetrical structures are presented to illustrate the main results. |
| first_indexed | 2024-03-09T18:36:29Z |
| format | Article |
| id | doaj.art-b1931a8c28774704a665b32e63b572c2 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T18:36:29Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-b1931a8c28774704a665b32e63b572c22023-11-24T07:07:17ZengMDPI AGSymmetry2073-89942022-10-011411225110.3390/sym14112251Singularities of Osculating Developable Surfaces of Timelike Surfaces along CurvesYongqiao Wang0Lin Yang1Pengcheng Li2Yuan Chang3Department of Mathematics, Dalian Maritime University, Dalian 116026, ChinaDepartment of Mathematics, Dalian Maritime University, Dalian 116026, ChinaSchool of Mathematics and Statistics, Northeast Normal University, Changchun 130024, ChinaSchool of Mathematics, Dongbei University of Finance and Economics, Dalian 116026, ChinaIn this paper, we focus on a developable surface tangent to a timelike surface along a curve in Minkowski 3-space, which is called the <i>osculating developable surface</i> of the timelike surface along the curve. The ruling of the osculating developable surface is parallel to the <i>osculating Darboux vector field</i>. The main goal of this paper is to classify the singularities of the osculating developable surface. To this end, two new invariants of curves are defined to characterize these singularities. Meanwhile, we also research the singular properties of osculating developable surfaces near their lightlike points. Moreover, we give a relation between osculating Darboux vector fields and normal vector fields of timelike surfaces along curves from the viewpoint of Legendrian dualities. Finally, some examples with symmetrical structures are presented to illustrate the main results.https://www.mdpi.com/2073-8994/14/11/2251osculating developable surfacesLorentzian support functionssingularitiesLegendrian dualities |
| spellingShingle | Yongqiao Wang Lin Yang Pengcheng Li Yuan Chang Singularities of Osculating Developable Surfaces of Timelike Surfaces along Curves Symmetry osculating developable surfaces Lorentzian support functions singularities Legendrian dualities |
| title | Singularities of Osculating Developable Surfaces of Timelike Surfaces along Curves |
| title_full | Singularities of Osculating Developable Surfaces of Timelike Surfaces along Curves |
| title_fullStr | Singularities of Osculating Developable Surfaces of Timelike Surfaces along Curves |
| title_full_unstemmed | Singularities of Osculating Developable Surfaces of Timelike Surfaces along Curves |
| title_short | Singularities of Osculating Developable Surfaces of Timelike Surfaces along Curves |
| title_sort | singularities of osculating developable surfaces of timelike surfaces along curves |
| topic | osculating developable surfaces Lorentzian support functions singularities Legendrian dualities |
| url | https://www.mdpi.com/2073-8994/14/11/2251 |
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