摘要
经典的欧拉公式描述了两曲面交线的曲率和曲面的法曲率以及曲面夹角之间的关系。本文给出了R3中曲面的法曲率的欧拉公式的简单证明。并得到一个关于曲面交线曲率及曲面测地曲率的类似的欧拉公式。
The classic Euler formula describes the relationships between the curvature of the intersection curve of two surfaces and the normal curvatures of surfaces and the angle between surfaces. In this paper, we give simplified proofs of the Euler formula for normal curvatures of surfaces of R3. We derive an analogue of Euler formula for geodesic curvatures of surfaces.
出处
《数学杂志》
CSCD
北大核心
2005年第4期355-357,共3页
Journal of Mathematics
基金
TheScientificResearchGrantofGuizhouProvinceofChina.
关键词
曲率
法曲率
测地曲率
Curvature
normal curvature
geodesic curvature
