A Surface Pencil with Bertrand Curves as Joint Curvature Lines in Euclidean Three-Space

IF 2.2 3区综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES

Symmetry-Basel Pub Date : 2023-10-27 DOI:10.3390/sym15111986

Sahar H. Nazra, Rashad A. Abdel-Baky

引用次数: 0

Abstract

The main outcome of this work is the construction of a surface pencil with a similarity to Bertrand curves in Euclidean 3-space E3. Then, by exploiting the Serret–Frenet frame, we deduce the sufficient and necessary conditions for a surface pencil with Bertrand curves as joint curvature lines. Consequently, the expansion to the ruled surface pencil is also designed. As demonstrations of our essential findings, we illustrate some models to emphasize the process.

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欧几里得三维空间中以Bertrand曲线为联合曲率线的曲面铅笔

这项工作的主要成果是在欧几里得三维空间E3中构造一个与贝特朗曲线相似的表面铅笔。然后，利用Serret-Frenet框架，推导出以Bertrand曲线为关节曲率线的曲面铅笔的充要条件。因此，还设计了直纹面铅笔的扩展。为了演示我们的基本发现，我们举例说明了一些模型来强调这个过程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Symmetry-Basel MULTIDISCIPLINARY SCIENCES-

CiteScore

5.40

自引率

11.10%

发文量

2276

审稿时长

14.88 days

期刊介绍： Symmetry (ISSN 2073-8994), an international and interdisciplinary scientific journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced.