| 曲面上曲线为短程线的必要条件的证明方法 |
| |
| 引用本文： | 张光照,邢家省,贺慧霞.曲面上曲线为短程线的必要条件的证明方法[J].河南科学,2013(12):2126-2132. |
| |
| 作者姓名： | 张光照 邢家省 贺慧霞 |
| |
| 作者单位： | [1]河南经贸职业学院技术科学系,郑州450000 [2]北京航空航天大学数学与系统科学学院,数学、信息与行为教育部重点实验室,北京100191 |
| |
| 基金项目： | 国家自然科学基金资助项目（11201020） |
| |
| 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．
|
| 关 键 词： | 弧长参数 测地线 曲面上短程线 变分方法 |
The Necessary Condition of a Curve Being a Shortest-line on Surfaces |
| |
| Zhang Guangzhao,Xing Jiasheng,He Huixia.The Necessary Condition of a Curve Being a Shortest-line on Surfaces[J].Henan Science,2013(12):2126-2132. |
| |
| Authors: | Zhang Guangzhao Xing Jiasheng He Huixia |
| |
| Institution: | 1. The Department of Technology Science, Henan Economy ＆ Trade Vocational College, Zhengzhou 450000, China; 2. Department of Mathematics, LMIB of the Ministry of Education, Beihang University, Beijing 100191, China |
| |
| Abstract: | 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. |
| |
| Keywords: | the arc-length parameter geodesics the shortest line variational method |
| 本文献已被 维普 等数据库收录！ |
