十字帽的对称性

IF 0.4 4区数学 Q4 MATHEMATICS

Tohoku Mathematical Journal Pub Date : 2021-05-05 DOI:10.2748/tmj.20211203

Atsufumi Honda, K. Naokawa, K. Saji, M. Umehara, Kotaro Yamada

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引用次数: 0

摘要

众所周知，欧氏3空间中曲面上的十字帽可以用Bruce West的法线形式表示，这是一个以奇异点为中心的特殊局部坐标系。在本文中，我们展示了这样一个坐标系的某种唯一性。特别地，与该坐标系相关联的函数在交叉帽奇异点上产生新的不变量。利用它们，我们对十字帽上可能的对称性进行了分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Symmetries of cross caps

It is well-known that cross caps on surfaces in the Euclidean 3-space can be expressed in Bruce-West's normal form, which is a special local coordinate system centered at the singular point. In this paper, we show a certain kind of uniqueness of such a coordinate system. In particular, the functions associated with this coordinate system produce new invariants on cross cap singular points. Using them, we classify the possible symmetries on cross caps.

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