| 高维球面曲线 |
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| 引用本文： | 欧业林.高维球面曲线[J].哈尔滨师范大学自然科学学报,1990,6(4):13-19. |
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| 作者姓名： | 欧业林 |
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| 作者单位： | 广西民族学院 |
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| 摘 要： | 本文研究高维球面曲线的性质.在给出一个特别的活动标架及其无穷小位移公式(定理1)之后,我们证明了高维球面曲线落于赤道上的一个充要条件(定理2).我们还给出了高维球面曲线的几个特征性质.
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| 关 键 词： | 高维球面曲线 活动标架 曲率 |
ON HIGHER DIMENTIONAL SPHERICAL CURVES |
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| Qu Yelin Guangxi Institute For Nationalities.ON HIGHER DIMENTIONAL SPHERICAL CURVES[J].Natural Science Journal of Harbin Normal University,1990,6(4):13-19. |
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| Authors: | Qu Yelin Guangxi Institute For Nationalities |
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| Institution: | Qu Yelin Guangxi Institute For Nationalities |
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| Abstract: | We study, in this paper, the properties of a curve ?(s)in S~(n-1), a sphere in 1R~n. First, we give, on ?(s)?S~(n-1), a special moving frame and the formula for the infinitesimal change of the frame (Theorem 1). Then we obtain a necessary and sufficient condition for ?(s)to lie completely on S~(n-2) (Theorem 2). Finally, we turn to the curves in S~?, and give several results which characterizes the curvatures of a curve in S~?. |
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| Keywords: | : Higher dimentional spherical curve Moving frame Higher curvatures |
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