关键词： 高斯曲率, 测地曲率, 正交曲线坐标网, 高斯-波涅公式

Abstract: 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.

Key words: Gaussian curvature, geodesic curvature, coordinate grid of the orthogonal curve, Gauss-Bonnet formula