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Keywords = isoasymptotic curve

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9 pages, 1284 KiB  
Article
Surfaces Family with Bertrand Curves as Common Asymptotic Curves in Euclidean 3–Space E3
by Maryam T. Aldossary and Rashad A. Abdel-Baky
Symmetry 2023, 15(7), 1440; https://doi.org/10.3390/sym15071440 - 18 Jul 2023
Cited by 2 | Viewed by 1531
Abstract
The main result of this paper is constructing a surfaces family with the similarity of Bertrand curves in Euclidean 3–space E3. Then, by utilizing the Serret–Frenet frame, we conclude the sufficient and necessary conditions of surfaces family interpolating Bertrand curves as [...] Read more.
The main result of this paper is constructing a surfaces family with the similarity of Bertrand curves in Euclidean 3–space E3. Then, by utilizing the Serret–Frenet frame, we conclude the sufficient and necessary conditions of surfaces family interpolating Bertrand curves as common asymptotic curves. Consequently, the expansion to the ruled surfaces family is also depicted. As implementations of our main results, we demonstrate some examples to confirm the method. Full article
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