一般方程表示下曲面上曲线测地曲率的计算公式及其应用  

Calculation formula of the geodesic curvature of a curve on a surface represented by the general equation and its applications

作　　者：梁钊 张量 LIANG Zhao;ZHANG Liang(School of Mathematics and Statistics,Anhui Normal University,Wuhu 241002,China)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241002

出　　处：《高师理科学刊》2023年第1期10-13,19,共5页Journal of Science of Teachers＇College and University

摘　　要：测地曲率是经典微分几何曲面理论中一个重要的内蕴几何量,测地曲率恒为零的曲线即曲面上的测地线.给出了一般方程表示下曲面上曲线测地曲率的计算公式,利用该计算公式给出了椭球面上圆截线问题的一种微分几何解决方法.Geodesic curvature is an important intrinsic geometric quantity in the theory of surfaces in classical differential geometry,and it is known that a curve with constant zero geodesic curvature is a geodesic on a surface.A formula of the geodesic curvature of a curve on a surface represented by the general equation was given,and it was used to give a differential geometric solution to the circular transection problem on an ellipsoid.

关 键 词：测地曲率 椭球面 圆截线 

分 类 号：O186.11[理学—数学]