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

Author

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  • Nidal Echabbi
  • Amina Ouazzani Chahdi

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.

Suggested Citation

  • Nidal Echabbi & Amina Ouazzani Chahdi, 2021. "Some Special Ruled Surfaces Generated by a Direction Curve according to the Darboux Frame and their Characterizations," Abstract and Applied Analysis, Hindawi, vol. 2021, pages 1-12, September.
    • Handle: RePEc:hin:jnlaaa:8624794
    DOI: 10.1155/2021/8624794
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