A note on striction curves
| Autor: | Absos Ali Shaikh, Pinaki Ranjan Ghosh |
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| Rok vydání: | 2023 |
| DOI: | 10.21203/rs.3.rs-2607086/v1 |
| Popis: | In this paper, we have studied the striction curves of a normal ruled surface. We have shown that the evolute of a base curve is the striction curve of a normal ruled surface and the singularities of such surface lie on the evolute of the base curve. We have proved that the striction curves orthogonally cut the planar base curves. Also, we have proved that the surface area between a planar base curve and striction curve of a normal ruled surface is identical to the surface area between the evolutes of the base curve and striction curve. We have obtained different conditions for which the striction curve coincides with the base curve of some ruled surfaces. We have proved that the striction curve of a tangential Darboux developable of a space curve coincides with the base curve if and only if the space curve is a helix. We have deduced a beautiful form of surface area between the base curve and striction curve of a tangential Darboux developable. |
| Databáze: | OpenAIRE |
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