摘要
考虑曲面上的短程线的性质问题,运用曲面上曲线的向量表示和弧长公式,由直接的变分方法,给出了曲面上曲线为短程线时所满足的微分方程.
In this paper, we considered the shortest line between two points on surfaces in 3-dimension Euclidean space. By using the variational methods and the arc-length formula,we gave several easier ways to prove some properties of these lines and show the relations between these lines and the geodesics. The differential equations of the shortest line are also derived.
出处
《河南科学》
2013年第12期2126-2132,共7页
Henan Science
基金
国家自然科学基金资助项目(11201020)
关键词
弧长参数
测地线
曲面上短程线
变分方法
the arc-length parameter
geodesics
the shortest line
variational method.
