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

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Published: Oct 30, 2021
DOI: https://doi.org/10.5556/j.tkjm.52.2021.3463
Keywords:
Frenet equations, Intrinsic equations, k-slant helices, Position vector.

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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.

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.




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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
Issue
Vol. 52 No. 4 (2021)
Section
Papers
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