Geometry of special curves and surfaces in 3-space form
Geometry of special curves and surfaces in 3-space form
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三空间形式的特殊曲线和曲面的几何
DOI：
10.1016/j.geomphys.2018.09.010
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发表时间：
2019
影响因子：
1.5
通讯作者：
Pei Donghe
中科院分区：
文献类型：
--
作者：
Huang Jie;Chen Liang;Izumiya Shyuichi;Pei Donghe
从曲面上的曲线出发，研究了三维空间形式中Bertrand曲线的微分几何。我们定义了一种由三维空间形式的测地线生成的特殊曲面，称为测地线曲面。这种曲面不是别的，而是三维欧氏空间中直纹曲面的推广。作为结果，我们证明了Bertrand曲线与主法测地曲面的平均曲率有关。
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.