On the Darboux ruled surface of a general helix in the Nil₃
Nil geometry is one of the eight geometries of Thurston's conjecture. In this paper we study in Nil 3-space and the Nil metric with respect to the standard coordinates (x,y,z) is gNil3=(dx)2+(dy)2+(dz-xdy)2 in IR3. In [8] we have already and out the explicit parametric equation of a general hel...
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BİSKA Bilisim Company
2016-01-01
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| Series: | New Trends in Mathematical Sciences |
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| Online Access: | https://ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=5104 |
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doaj-3233074fc167412dbf8688956ae350912020-11-24T21:07:18ZengBİSKA Bilisim CompanyNew Trends in Mathematical Sciences2147-55202147-55202016-01-0141152410.20852/ntmsci.20161156175104On the Darboux ruled surface of a general helix in the Nil₃Şeyda KILICOGLU0Şeyda KILICOGLU1Baskent UniversityBaskent UniversityNil geometry is one of the eight geometries of Thurston's conjecture. In this paper we study in Nil 3-space and the Nil metric with respect to the standard coordinates (x,y,z) is gNil3=(dx)2+(dy)2+(dz-xdy)2 in IR3. In [8] we have already and out the explicit parametric equation of a general helix and Frenet vector yields, with first and second curvatures k1 and k2; respectively, in Nil 3-Space. Here we and out the parametric equations of the Darboux ruled surface of the general helix in Nil Space Nil3:https://ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=5104Nil spacegeneral helixruled surface |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Şeyda KILICOGLU Şeyda KILICOGLU |
| spellingShingle |
Şeyda KILICOGLU Şeyda KILICOGLU On the Darboux ruled surface of a general helix in the Nil₃ New Trends in Mathematical Sciences Nil space general helix ruled surface |
| author_facet |
Şeyda KILICOGLU Şeyda KILICOGLU |
| author_sort |
Şeyda KILICOGLU |
| title |
On the Darboux ruled surface of a general helix in the Nil₃ |
| title_short |
On the Darboux ruled surface of a general helix in the Nil₃ |
| title_full |
On the Darboux ruled surface of a general helix in the Nil₃ |
| title_fullStr |
On the Darboux ruled surface of a general helix in the Nil₃ |
| title_full_unstemmed |
On the Darboux ruled surface of a general helix in the Nil₃ |
| title_sort |
on the darboux ruled surface of a general helix in the nil₃ |
| publisher |
BİSKA Bilisim Company |
| series |
New Trends in Mathematical Sciences |
| issn |
2147-5520 2147-5520 |
| publishDate |
2016-01-01 |
| description |
Nil geometry is one of the eight geometries of Thurston's conjecture. In this paper we study in Nil 3-space and the Nil metric with respect to the standard coordinates (x,y,z) is gNil3=(dx)2+(dy)2+(dz-xdy)2 in IR3. In [8] we have already and out the explicit parametric equation of a general
helix and Frenet vector yields, with first and second curvatures k1 and k2; respectively, in Nil 3-Space. Here we and out the parametric equations of the Darboux ruled surface of the general helix in Nil Space Nil3: |
| topic |
Nil space general helix ruled surface |
| url |
https://ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=5104 |
| work_keys_str_mv |
AT seydakilicoglu onthedarbouxruledsurfaceofageneralhelixinthenil3 AT seydakilicoglu onthedarbouxruledsurfaceofageneralhelixinthenil3 |
| _version_ |
1716763391318556672 |