Some Special Ruled Surfaces Generated by a Direction Curve according to the Darboux Frame and their Characterizations
Open Access
- 11 September 2021
- journal article
- research article
- Published by Hindawi Limited in Abstract and Applied Analysis
- Vol. 2021, 1-12
- https://doi.org/10.1155/2021/8624794
Abstract
In this work, we consider the Darboux frame of a curve lying on an arbitrary regular surface and we construct ruled surfaces having a base curve which is a -direction curve. Subsequently, a detailed study of these surfaces is made in the case where the directing vector of their generatrices is a vector of the Darboux frame, a Darboux vector field. Finally, we give some examples for special curves such as the asymptotic line, geodesic curve, and principal line, with illustrations of the different cases studied.Keywords
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