| 三维欧氏空间中曲线和曲面的运动不变特征 |
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| 引用本文： | 蔡惠京,周俊英.三维欧氏空间中曲线和曲面的运动不变特征[J].广东广播电视大学学报,2010,19(6):106-110. |
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| 作者姓名： | 蔡惠京 周俊英 |
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| 作者单位： | 中山广播电视大学,广东中山528405 |
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| 摘 要： | 三维欧氏空间中曲线的曲率在三维空间的运动下是不变的，但挠率却可以相差一个符号。类似地，曲面的第一基本形式在运动下是不变的，但第二基本形式却可以相差一个符号；尽管如此，高斯曲率却是运动不变的。
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| 关 键 词： | 欧氏空间 曲线 曲率 曲面 运动 |
On the Motional Invariants of Curves and Surfaces in the Euclidean 3-Space |
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| CAI Hui-jing,ZHOU Jun-ying.On the Motional Invariants of Curves and Surfaces in the Euclidean 3-Space[J].Journal of Guangdong Radio & Television University,2010,19(6):106-110. |
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| Authors: | CAI Hui-jing ZHOU Jun-ying |
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| Institution: | (Zhongshan Radio ＆ TV University, Zhongshan, Guangdong, China, 528403) |
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| Abstract: | In this paper, it is proved that, under a motion of space, the curvature of a curve in the Euclidean space does not change, but the torsion can be changed by multiplied -1. Similarly, it is proved that, under a motion of space, the first fundamental form of a surface does not change, but the second fundamental form can be changed by multiplied -1. However the Gaussian curvature is a motional invariant. |
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| Keywords: | Euclidean space curve curvature surface motion |
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