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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| Format: | Article |
| Language: | English |
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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 |
| Summary: | 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: |
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| ISSN: | 2147-5520 2147-5520 |