Translation surfaces generated by the spherical indicatrices of Frenet frame of regular curves of 3-dimensional Euclidean space

Salma Khan; Malika Izid; Soukaina Ouarab; Amina Ouazzani Chahdi

doi:10.5269/bspm.68555

Salma Khan University of Hassan II-Casablanca https://orcid.org/0009-0000-4143-2035
Malika Izid University of Hassan II-Casablanca https://orcid.org/0000-0001-9509-6348
Soukaina Ouarab University of Hassan I-Settat https://orcid.org/0000-0001-5854-1553
Amina Ouazzani Chahdi University of Hassan II-Casablanca https://orcid.org/0000-0002-3390-5338

Abstract

In this paper, we are interested in translation surfaces generated by the principal normals of two regular curves provided with their alternative frames, and consequently, we generalize this study to confirm the results obtained. Moreover, we give the position vector with illustrations for these surfaces, in some special cases, where the two regular curves are respectively general helices, slant helices, and slant-slant helices.

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