On the parallel surfaces of the non-developable surfaces
In the differential geometry of curves and surfaces, the curvatures of curves and surfaces are often calculated and results are given. In particular, the results given by using the apparatus of the curve - surface pair are important in terms of what kind of surface the surface indicates. In this st...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2020-06-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/359 |
| _version_ | 1827395648735936512 |
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| author | Ali ¸Cakmak Yusuf Yaylı |
| author_facet | Ali ¸Cakmak Yusuf Yaylı |
| author_sort | Ali ¸Cakmak |
| collection | DOAJ |
| description |
In the differential geometry of curves and surfaces, the curvatures of curves and surfaces are often calculated and results are given. In particular, the results given by using the apparatus of the curve - surface pair are important in terms of what kind of surface the surface indicates. In this study, some relationships between curvatures of the parallel surface pair ( X,Xr ) via structure functions of non - developable ruled surface X ( u,v ) = a ( u ) + vb ( u ) are established such that a ( u ) is striction curve of non - developable surface and b ( u ) is a unit spherical curve in E 3. Especially, it is examined whether the non - developable surface Xr is minimal surface, linear Weingarten surface and Weingarten surface. X and its parallel Xr are expressed on the Helicoid surface sample. It is indicated on the figure with the help of S W P. Moreover, curvatures of curve - surface pairs ( X,a ) and ( Xr,β ) are investigated and some conclusions are obtained.
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| first_indexed | 2024-03-08T18:38:45Z |
| format | Article |
| id | doaj.art-2a7a27ffb2924db6971fb088a3482f1f |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:38:45Z |
| publishDate | 2020-06-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-2a7a27ffb2924db6971fb088a3482f1f2023-12-29T10:20:20ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112020-06-01982On the parallel surfaces of the non-developable surfacesAli ¸CakmakYusuf Yaylı In the differential geometry of curves and surfaces, the curvatures of curves and surfaces are often calculated and results are given. In particular, the results given by using the apparatus of the curve - surface pair are important in terms of what kind of surface the surface indicates. In this study, some relationships between curvatures of the parallel surface pair ( X,Xr ) via structure functions of non - developable ruled surface X ( u,v ) = a ( u ) + vb ( u ) are established such that a ( u ) is striction curve of non - developable surface and b ( u ) is a unit spherical curve in E 3. Especially, it is examined whether the non - developable surface Xr is minimal surface, linear Weingarten surface and Weingarten surface. X and its parallel Xr are expressed on the Helicoid surface sample. It is indicated on the figure with the help of S W P. Moreover, curvatures of curve - surface pairs ( X,a ) and ( Xr,β ) are investigated and some conclusions are obtained. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/359parallel surfacesnon-developable ruled surfacestriction lineGaussian curvaturemean curvaturecurvatures of curve-surface pair |
| spellingShingle | Ali ¸Cakmak Yusuf Yaylı On the parallel surfaces of the non-developable surfaces Қарағанды университетінің хабаршысы. Математика сериясы parallel surfaces non-developable ruled surface striction line Gaussian curvature mean curvature curvatures of curve-surface pair |
| title | On the parallel surfaces of the non-developable surfaces |
| title_full | On the parallel surfaces of the non-developable surfaces |
| title_fullStr | On the parallel surfaces of the non-developable surfaces |
| title_full_unstemmed | On the parallel surfaces of the non-developable surfaces |
| title_short | On the parallel surfaces of the non-developable surfaces |
| title_sort | on the parallel surfaces of the non developable surfaces |
| topic | parallel surfaces non-developable ruled surface striction line Gaussian curvature mean curvature curvatures of curve-surface pair |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/359 |
| work_keys_str_mv | AT alicakmak ontheparallelsurfacesofthenondevelopablesurfaces AT yusufyaylı ontheparallelsurfacesofthenondevelopablesurfaces |