摘要
首先将常曲率曲面上一些基本的三角公式改写成统一的形式.然后定义了常曲率曲面上测地线集的密度,通过常曲率曲面上的三角公式以及参数变换证明了该密度与坐标选取无关.最后给出了常曲率曲面上测地线集密度的几种形式.
In this paper,some basic trigonometric formulae on the surface of constant curvature are rewritten into unified forms.Then the density of the sets of geodesics on the surface of constant curvature is defined,and it is proved that the density is independent of the choice of coordinates by the trigonometric formulae and parameter variations.Some other forms of the density are also given.
作者
张芷若
冯书香
ZHANG Zhi-ruo;FENG Shu-xiang(School of Mathematics and Statistics, Southwest University, Chongqing 400715, China)
出处
《西南师范大学学报(自然科学版)》
CAS
2021年第6期42-46,共5页
Journal of Southwest China Normal University(Natural Science Edition)
基金
国家自然科学基金项目(11971415).
关键词
常曲率曲面
测地线密度
三角公式
the surface of constant curvature
density of geodesics
trigonometric formulae