Framed Surfaces in the Euclidean Space
Framed Surfaces in the Euclidean Space
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DOI：
10.1007/s00574-018-0090-z
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发表时间：
2017-06
期刊：
影响因子：
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通讯作者：
Tomonori Fukunaga;Masatomo Takahashi
中科院分区：
文献类型：
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作者：
Tomonori Fukunaga;Masatomo Takahashi
框架曲面是欧氏空间中具有移动框架的光滑曲面。框架表面可以具有奇点。我们处理光滑曲面的奇异点，即奇异曲面更直接。利用活动标架，给出了标架曲面的基本不变量和曲率。然后证明了框架曲面基本不变量的存在唯一性。我们给出了框架曲面的性质和典型例子。此外，我们构造框架曲面作为单参数族的Legendre曲线沿着框架曲线。利用Legendre曲线和框架曲线的曲率，给出了框架曲面奇点的一个判别准则。
A framed surface is a smooth surface in the Euclidean space with a moving frame. The framed surfaces may have singularities. We treat smooth surfaces with singular points, that is, singular surfaces more directly. By using the moving frame, the basic invariants and curvatures of the framed surface are introduced. Then we show that the existence and uniqueness for the basic invariants of the framed surfaces. We give properties of framed surfaces and typical examples. Moreover, we construct framed surfaces as one-parameter families of Legendre curves along framed curves. We give a criteria for singularities of framed surfaces by using the curvature of Legendre curves and framed curves.