《微分几何》中关于主方向的注记  

A Note on the Principal Directions in Differential Geometry

作　　者：卢爱红[1] 刘建成[2] 

机构地区：[1]兰州职业技术学院经济管理系 [2]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《河西学院学报》2014年第5期18-21,共4页Journal of Hexi University

基　　金：国家自然科学基金项目(11261051)资助课题

摘　　要：熟知欧氏参数曲面在非脐点处有且仅有两个相互垂直的主方向.对相互垂直的理解是容易的,但文献[3]的处理方法在实际教学中,学生理解主方向只有两个时存在模糊之处.本文目的是仔细分析这些模糊之处及产生的原因,并给出较为清晰的补充修缮,以更好地为教学服务.It is known that there are exactly two perpendicular principal directions at a non umbilical point on a parameterized surface. It is easy to understand that the two principal directions are perpendicular. However, omissions and ambiguities still exist in[3] concerning to explain why there are exactly two principal directions. This paper tries to analyze the reasons and clean omissions and ambiguities, aiming to serve the teaching well.

关 键 词：参数曲面 主方向 正交 共轭 

分 类 号：O186.12[理学—数学]