Existence conditions of framed curves for smooth curves
Existence conditions of framed curves for smooth curves
复制标题
光滑曲线的框架曲线的存在条件
DOI：
10.1007/s00022-017-0371-5
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发表时间：
2017
影响因子：
0.6
通讯作者：
Masatomo Takahashi
中科院分区：
文献类型：
--
作者：
Tomonori Fukunaga;Masatomo Takahashi
框架曲线是欧几里得空间中具有移动框架的光滑曲线。我们称欧氏空间中的光滑曲线为框基曲线。本文给出了框架曲线存在的一个条件。实际上，我们构造了一条框架曲线，使得框架基础曲线的图像在一定条件下与给定光滑曲线的图像重合。因此，欧几里得平面中的多边形不仅可以实现为光滑曲线，还可以实现为有框的基本曲线。
A framed curve is a smooth curve in the Euclidean space with a moving frame. We call the smooth curve in the Euclidean space the framed base curve. In this paper, we give an existence condition of framed curves. Actually, we construct a framed curve such that the image of the framed base curve coincides with the image of a given smooth curve under a condition. As a consequence, polygons in the Euclidean plane can be realised as not only a smooth curve but also a framed base curve.