有向曲线切曲面的奇点
微分几何
2016-08-02 v2
摘要
有向曲线是沿曲线具有明确定义切线的可能奇异曲线。那么，只要环境空间被赋予任何仿射联络，有向曲线的切曲面就自然地被定义为曲线的切测地线所构成的直纹曲面。本文完成了通用有向曲线的局部微分同胚分类。结果表明，燕尾和开燕尾在切曲面奇点的分类中通用地出现。
引用
@article{arxiv.1607.08702,
title = {Singularities of tangent surfaces to directed curves},
author = {G. Ishikawa and T. Yamashita},
journal= {arXiv preprint arXiv:1607.08702},
year = {2016}
}
备注
This paper is a second half of the unpublished paper arXiv:1501.07341 [math.DG], which is divided into two shorter papers, the paper arXiv:1602.02458 [math.DG] (to appear in Journal of Geometry) and the present paper