球面上简单闭曲线的等周不等式  

Isoperimetric Inequality of Simple Spherical Closed Curve

作　　者：闫德宝[1] 

机构地区：[1]山东菏泽学院数学系,山东菏泽274015

出　　处：《云南农业大学学报》2011年第5期723-724,729,共3页Journal of Yunnan Agricultural University

摘　　要：等周不等式反映了周长固定的闭曲线其周长和所围区域面积之间的关系。本文通过适当选取球面上单位法向量的方向,即由球面指向球心,得到球面曲线曲率及测地曲率的表达式,利用曲面上的高斯-波涅公式在球面上推广了该不等式。Isoperimetric inequality shows the relation of perimter and area that the closed curve edcircles with its perimeter fixed.In this paper,the author get curvature and geodesic curvature of spherical closed curves by selecting properly the direction of unit normal vector on the sphere,that is,from sphere to the center of its.Using Gass-Bonnet Formular the isoperimetric inequality of simple spherical closed curve is promoted.

关 键 词：球面闭曲线 等周不等式 高斯-波涅公式 测地曲率 

分 类 号：O186.11[理学—数学]