Singularities of spherical surface in R4

IF 1 4区数学 Q1 MATHEMATICS Open Mathematics Pub Date : 2024-08-10 DOI:10.1515/math-2024-0033

Haiming Liu, Yuefeng Hua, Wanzhen Li

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Abstract

In this article, we mainly study the geometric properties of spherical surface of a curve on a hypersurface

\Sigma

in four-dimensional Euclidean space. We define a family of tangent height functions of a curve on

\Sigma

as the main tool for research and combine the relevant knowledge of singularity theory. It is shown that there are three types of singularities of spherical surface, that is, in the local sense, the spherical surface is respectively diffeomorphic to the cuspidal edge, the swallowtail, and the cuspidal beaks. In addition, we give two examples of the spherical surface.

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R4 中球面的奇异点

本文主要研究四维欧几里得空间中超曲面 Σ \Sigma 上曲线球面的几何性质。我们定义了 Σ \Sigma 上曲线的切高函数族作为主要研究工具，并结合奇点理论的相关知识。研究表明，球面存在三种奇异性，即在局部意义上，球面分别衍射为尖顶边、燕尾和尖顶喙。此外，我们还举了两个球面的例子。

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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来源期刊

Open Mathematics MATHEMATICS-

CiteScore

2.40

自引率

5.90%

发文量

审稿时长

16 weeks

期刊介绍： Open Mathematics - formerly Central European Journal of Mathematics Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant, original and relevant works in all areas of mathematics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, language-correction services, no space constraints and immediate publication. Open Mathematics is listed in Thomson Reuters - Current Contents/Physical, Chemical and Earth Sciences. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind. Aims and Scope The journal aims at presenting high-impact and relevant research on topics across the full span of mathematics. Coverage includes: