Position Vectors of Curves Generalizing General Helices and Slant Helices in Euclidean 3-Space

Authors

  • Abderrazak El Haimi Departement of Mathematics and Informatic, Faculty of Sciences Ben M’Sik, University of Hassan II- Casablanca, Morrocco
  • Malika Izid FSBM https://orcid.org/0000-0001-9509-6348
  • Amina Ouazzani Chahdi Departement of Mathematics and Informatic, Faculty of Sciences Ben M’Sik, University of Hassan II- Casablanca, Morrocco.

DOI:

https://doi.org/10.5556/j.tkjm.52.2021.3463

Keywords:

Frenet equations, Intrinsic equations, k-slant helices, Position vector.

Abstract

In this paper, we give a new characterization of a k-slant helix which is a generalization of general helix and slant helix. Thereafter, we construct a vector differential equation of the third order to determine the parametric representation of a k-slant helix according to standard frame in Euclidean 3-space. Finally, we apply this method to find the position vector of some examples of 2-slant helix by means of intrinsic equations.

References

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Published

2021-10-30

How to Cite

Haimi, A. E., Izid, M., & Chahdi, A. O. (2021). Position Vectors of Curves Generalizing General Helices and Slant Helices in Euclidean 3-Space. Tamkang Journal of Mathematics, 52(4), 467-478. https://doi.org/10.5556/j.tkjm.52.2021.3463

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Section

Papers