Surfaces Family with Bertrand Curves as Common Asymptotic Curves in Euclidean 3-Space E3

被引：1
|
作者：
Aldossary, Maryam T. [1 ]
Abdel-Baky, Rashad A. [2 ]
机构：
[1] Imam Abdulrahman bin Faisal Univ, Coll Sci, Dept Math, POB 1982, Damam, Saudi Arabia
[2] Univ Assiut, Fac Sci, Dept Math, Assiut 71516, Egypt
来源：
SYMMETRY-BASEL | 2023年 / 15卷 / 07期
关键词：
Bertrand mate; Dirichlet approach; isoasymptotic curve; PARAMETRIC REPRESENTATION; PENCIL; LINE;
D O I：
10.3390/sym15071440
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The main result of this paper is constructing a surfaces family with the similarity of Bertrand curves in Euclidean 3-space E-3. 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.
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页数：9
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