Geometry of special curves and surfaces in 3-space form

JOURNAL OF GEOMETRY AND PHYSICS

卷:136

Article

Huang, Jie¹  Chen, Liang¹  Izumiya, Shyuichi²  Pei, Donghe¹ 

[1] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China

[2] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan

关键词: Bertrand curve;    Space form;    Mean curvature;    Geodesic;   

DOI  :  10.1016/j.geomphys.2018.09.010

来源: Elsevier

【 摘 要 】

We investigate differential geometry of Bertrand curves in 3-dimensional space form from a viewpoint of curves on surfaces. We define a special kind of surface, named geodesic surface, generated by geodesics in 3-dimensional space form. This kind of surface is nothing else, but a generalization of ruled surface in 3-dimensional Euclidean space. As results, we show that the Bertrand curve is related to the mean curvature of principal normal geodesic surface. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free