曲面上曲线为短程线的必要条件的证明方法  

The Necessary Condition of a Curve Being a Shortest-line on Surfaces

作　　者：张光照[1] 邢家省[2] 贺慧霞[2] 

机构地区：[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

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)

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.

关 键 词：弧长参数 测地线 曲面上短程线 变分方法 

分 类 号：O186.1[理学—数学]