曲面上的高斯曲率与高斯-波涅公式

Gaussian Curvature of Curved Surface and Gauss-Bonnet Formula

考虑曲面上高斯曲率计算公式的使用方法问题,给出椭球面上高斯曲率的求法;在曲面正交曲线坐标网下,给出高斯-波涅公式的证明过程,并指出高斯曲率简化公式的来源;由高斯曲率的曲面积分结果,导出曲面积分的一些几何意义.

With consideration given to the application method of Gaussian curvature computation formula to curved surface,a technique is suggested for solving Gaussian curvature of ellipsoids.By using curved surface coordinate grid of the orthogonal curve,the proving process of Gauss-Bonnet formula is shown and the source of a simplified Gaussian curvature formula is also pointed out.From the surface integral results of Gaussian curvature,some geometrical meanings are derived for surface integral.