A New Approach to Mannheim Curve in Euclidean 3-Space

IF 0.7 Q2 MATHEMATICS

Tamkang Journal of Mathematics Pub Date : 2021-11-10 DOI:10.5556/j.tkjm.54.2023.4085

A. Uçum, Ç. Camcı, K. Ilarslan

引用次数: 2

Abstract

In this article, a new approach is given for Mannheim curves in 3-dimensional Euclidean space. Thanks to this approach, the necessary and sufficient conditions including the known results have been obtained for a curve to be Mannheim curve in E³. In addition, related examples and graphs are given by showing that there can be Mannheim curves in Salkowski or anti-Salkowski curves as well as giving Mannheim mate curves, which are not in literature. Finally, the Mannheim partner curves are characterized in E³.

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欧几里得三维空间中曼海姆曲线的一种新方法

本文给出了三维欧几里得空间中求解曼海姆曲线的一种新方法。通过这种方法，得到了曲线在E³中为曼海姆曲线的充分必要条件，包括已知的结果。并给出了相关的例子和图表，说明Salkowski曲线或反Salkowski曲线中可能存在Mannheim曲线，并给出了文献中没有的Mannheim曲线。最后，用E³表示了曼海姆伙伴曲线。

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

Tamkang Journal of Mathematics MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量

期刊介绍： To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.