曲面上一类闭曲线的旋转指标公式  

On the Rotation Index Formulae of a Class of Closed Curves on a Surface

作　　者：李明[1] 

机构地区：[1]重庆理工大学数学与统计学院,重庆400054

出　　处：《西南大学学报（自然科学版）》2013年第8期97-100,共4页Journal of Southwest University(Natural Science Edition)

基　　金：重庆市自然科学基金资助项目(cstc2011jjA00026);重庆理工大学科研启动项目(01-60-37)

摘　　要：通过考虑闭曲线的简单分解,得到具有简单分解的闭曲线环绕数的旋转指标表示.给出了函数在具有简单分解的闭曲线所界定的区域上的积分表示.应用上述积分公式以及Gauss-Bonnet公式,将平面闭曲线旋转指标的曲率积分表示推广到曲面的情形.Using the simple finite decomposition of closed curves,the winding number of a closed curve with finite decomposition is represented by rotation indexes.An integral formula about the functions on the area bounded by a closed curve with finite decomposition is given.Using this integral formula and the Gauss-Bonnet formula,the rotation index formulae for closed plane curves are generalized to the closed curves with simple finite decomposition on a surface.

关 键 词：闭曲线 有限简单分解 旋转指标 GAUSS-BONNET公式 

分 类 号：O186.1[理学—数学]