Rectifying curves in the three-dimensional sphere

被引：16

作者：

Lucas, Pascual ^{[1
]}

Antonio Ortega-Yaguees, Jose ^{[1
]}

机构：

[1] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 421卷 / 02期

关键词：

Rectifying curve; Generalized helix; Darboux vector; Conical surface; Developable surface; SPACE;

D O I：

10.1016/j.jmaa.2014.07.079

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Rectifying curves in R-3 were introduced by B.Y. Chen in 2003 as space curves whose position vector always lies in its rectifying plane. In this paper, we extend this definition, as well as several results about rectifying curves obtained by Chen and Dillen (2005) and Izumiya and Takeuchi (2004), to curves in the three-dimensional sphere. Our results give nice and relevant differences between spherical and Euclidean geometries. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：1855 / 1868

页数：14

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