Rectifying Curves in the Three-Dimensional Hyperbolic Space

被引：8

作者：

Lucas, Pascual ^{[1
]}

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

机构：

[1] Univ Murcia, Dept Matemat, Murcia, Spain

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2016年 / 13卷 / 04期

关键词：

Rectifying curve; conical surface; geodesic; helix; Darboux vector; developable surface;

D O I：

10.1007/s00009-015-0615-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

B. Y. Chen introduced rectifying curves in as space curves whose position vector always lies in its rectifying plane. Recently, the authors have extended this definition (as well as several results about rectifying curves) to curves in the three-dimensional sphere. In this paper, we study rectifying curves in the three-dimensional hyperbolic space, and obtain some results of characterization and classification for such kind of curves. Our results give interesting and significant differences between hyperbolic, spherical and Euclidean geometries.

引用

页码：2199 / 2214

页数：16

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