Generic bifurcations of framed curves in a space form and their envelopes
Generic bifurcations of framed curves in a space form and their envelopes
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DOI：
10.1016/j.topol.2011.09.024
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发表时间：
2010-02
期刊：
影响因子：
--
通讯作者：
G. Ishikawa
中科院分区：
文献类型：
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作者：
G. Ishikawa
对空间形式En+1，Sn+1，Hn+1中的单参数标架曲线族的通有奇点和分叉进行了分类.两种框架被认为是适应框架和密切框架。特别地，我们给出了与框架曲线相关的包络奇异性的分类结果。相关的信封和他们的奇异性进行了分类。以框架曲线的几何不变量为特征的。我们适用于整体问题的框架曲线和延伸问题的曲面边界在三个空间。推广了石川（2010）[12]中的结果。
The generic singularities and bifurcations are classified for one-parameter families of curves with frames in the space forms En+1,Sn+1,Hn+1. Two kinds of frames are considered; adapted frames and osculating frames. In particular, we give the classification results on the singularities of envelopes associated to framed curves. The associated envelopes and their singularities are classified. characterised in term of geometric invariants of framed curves. We apply to the global problem of framed curves and to the extension problem of surfaces with boundaries in three space. generalising the results obtained in Ishikawa (2010) [12].