Singularities of spherical surface in R4

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-10 DOI:10.1515/math-2024-0033

Haiming Liu, Yuefeng Hua, Wanzhen Li

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引用次数: 0

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.