欧几里得三维空间$ \mathbb{E}^{3} $中具有Bertrand对的互测地线曲面族对

IF 1.8 3区数学 Q1 MATHEMATICS AIMS Mathematics Pub Date : 2023-01-01 DOI:10.3934/math.20231047

Areej A. Almoneef, R. Abdel-Baky

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引用次数: 0

摘要

本工作的主要兴趣是在欧几里德三维空间$ \mathbb{E}^{3} $中构造具有Bertrand对对称性的曲面族对。然后，利用Serret-Frenet框架，得出曲面族对插值Bertrand对为互测地线曲线的充要条件。此外，还得到了直纹曲面族对的结论。同时，通过几个实例对该工作进行了论证。

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Surface family pair with Bertrand pair as mutual geodesic curves in Euclidean 3-space $ \mathbb{E}^{3} $

The main interest of this work is to construct surface family pair with the symmetry of Bertrand pair in Euclidean 3-space $ \mathbb{E}^{3} $. Then, by employing the Serret-Frenet frame, we conclude the sufficient and necessary conditions of surface family pair interpolating Bertrand pair as mutual geodesic curves. Moreover, the conclusion to ruled surface family pair is also obtained. Meanwhile, this work is demonstrated through several examples.

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来源期刊

AIMS Mathematics Mathematics-General Mathematics

CiteScore

3.40

自引率

13.60%

发文量

769

审稿时长

90 days

期刊介绍： AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.