黎曼曲率张量在曲面论方程中的应用  

Riemann Curvature Tensor in the Surface of Equation

作　　者：张晓彦[1] 刁光成[1] 

机构地区：[1]山西水利职业技术学院,山西运城044004

出　　处：《太原师范学院学报（自然科学版）》2010年第3期46-48,共3页Journal of Taiyuan Normal University:Natural Science Edition

摘　　要：文章在黎曼曲率张量的概念和性质的基础上通过论证黎曼曲率张量可以只用第一基本形式的系数来表示,从而把高斯曲率这个概念推广到比曲面更一般的二维黎曼空间中,使高斯曲率的运用范围更广.Based on the concept and characteristics of Riemann curvature tensor,the paper argues that the Riemannian curvature tensor can be expressed through the use of the basic forms,so that the concept of Gauss curvature will be able to be used in the two-dimensinal Riemann space,which is more general than the curved surface.And as a consequence,the Gauss curvature will be used in a wider range.

关 键 词：张量场 黎曼曲率张量 GAUSS曲率 

分 类 号：O186.1[理学—数学]