Singularities of tangent surfaces to space curves
Singularities of tangent surfaces to space curves
复制标题
空间曲线切面的奇点
DOI：
10.1007/s00022-016-0341-3
复制
发表时间：
2017
影响因子：
0.6
通讯作者：
Tatsuya Yamashita
中科院分区：
文献类型：
--
作者：
Goo Ishikawa;Tatsuya Yamashita
我们给出了完整的解决方案的局部同胚分类问题的一般奇点出现在切曲面，在尽可能广泛的情况下。我们解释切线测地线作为切线时，（半）黎曼度量，或更一般地说，一个仿射连接是在任意维的环境空间。然后，给定一条浸入曲线，通过曲线的切线测地线定义切线曲面为直纹曲面。我们应用由Kokubu，Rossman，Saji，Umehara，Yamada和Fujimori，Saji，Umehara，Yamada发现的正面奇点的表征，并发现由第一作者有关奇点开口的过程。
We give the complete solution to the local diffeomorphism classification problem of generic singularities which appear in tangent surfaces, in as wider situations as possible. We interpret tangent geodesics as tangent lines whenever a (semi-)Riemannian metric, or, more generally, an affine connection is given in an ambient space of arbitrary dimension. Then, given an immersed curve, we define the tangent surface as the ruled surface by tangent geodesics to the curve. We apply the characterization of frontal singularities found by Kokubu, Rossman, Saji, Umehara, Yamada, and Fujimori, Saji, Umehara, Yamada, and found by the first author related to the procedure of openings of singularities.