基于达布框架的方向曲线生成的几种特殊直纹曲面及其特征

Q3 Mathematics

Abstract and Applied Analysis Pub Date : 2021-09-11 DOI:10.1155/2021/8624794

Nidal Echabbi, Amina Ouazzani Chahdi

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引用次数: 0

摘要

在这项工作中，我们考虑了位于任意规则曲面上的曲线的Darboux框架T，V，U，并构造了具有基曲线的直纹曲面，该基曲线是V方向曲线。随后，在它们的母线的方向向量是Darboux框架的向量，即Darboux向量场的情况下，对这些曲面进行了详细的研究。最后，我们给出了一些特殊曲线的例子，如渐近线、测地线和主曲线，并举例说明了所研究的不同情况。

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Some Special Ruled Surfaces Generated by a Direction Curve according to the Darboux Frame and their Characterizations

In this work, we consider the Darboux frame T , V , U of a curve lying on an arbitrary regular surface and we construct ruled surfaces having a base curve which is a V -direction curve. Subsequently, a detailed study of these surfaces is made in the case where the directing vector of their generatrices is a vector of the Darboux frame, a Darboux vector field. Finally, we give some examples for special curves such as the asymptotic line, geodesic curve, and principal line, with illustrations of the different cases studied.

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来源期刊

Abstract and Applied Analysis 数学-数学

CiteScore

2.30

自引率

0.00%

发文量

审稿时长

3.5 months

期刊介绍： Abstract and Applied Analysis is a mathematical journal devoted exclusively to the publication of high-quality research papers in the fields of abstract and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimization theory, and control theory. Abstract and Applied Analysis supports the publication of original material involving the complete solution of significant problems in the above disciplines. Abstract and Applied Analysis also encourages the publication of timely and thorough survey articles on current trends in the theory and applications of analysis.