Associated curves of a Frenet curve and their applications

被引：53

作者：

Choi, Jin Ho ^{[1
]}

Kim, Young Ho ^{[1
]}

机构：

[1] Kyungpook Natl Univ, Dept Math, Taegu 702701, South Korea

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2012年 / 218卷 / 18期

基金：

新加坡国家研究基金会;

关键词：

Associated curve; Principal-direction curve; Principal-donor curve; General helix; Slant helix; PD-rectifying curve; Bertrand curve;

D O I：

10.1016/j.amc.2012.02.064

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the notion of the principal (binormal)-direction curve and principal (binormal)-donor curve of a Frenet curve in E-3 and give the relationship of curvature and torsion of its mates. As application, we characterize general helices and slant helices in terms of their associated curves and give a canonical method to construct them. Also, we give a new characterization of Bertrand curve. Crown Copyright (C) 2012 Published by Elsevier Inc. All rights reserved.

引用

页码：9116 / 9124

页数：9

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