Some Special Ruled Surfaces Generated by a Direction Curve according to the Darboux Frame and their Characterizations

Nidal Echabbi and Amina Ouazzani Chahdi

Abstract and Applied Analysis, 2021, vol. 2021, 1-12

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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:8624794

DOI: 10.1155/2021/8624794

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