| 《微分几何》中关于主方向的注记 |
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| 引用本文： | 卢爱红,刘建成.《微分几何》中关于主方向的注记[J].河西学院学报,2014(5):18-21. |
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| 作者姓名： | 卢爱红 刘建成 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金项目(11261051)资助课题 |
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| 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。
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| 关 键 词： | 参数曲面 主方向 正交 共轭 |
A Note on the Principal Directions in Differential Geometry |
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| Lu Ai-hong,Liu Jian-cheng.A Note on the Principal Directions in Differential Geometry[J].Journal of Hexi University,2014(5):18-21. |
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| Authors: | Lu Ai-hong Liu Jian-cheng |
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| Institution: | Lu Ai-hong, Liu Jian-cheng (1. Department of Economy Management, Lanzhou Vocational Technical College, Lanzhou 730070; 2. School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070) |
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| Abstract: | 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 in3] 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. |
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| Keywords: | Parametric surface Principal direction Conjugate |
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