Geometry of the parabolic subset of generically immersed 3-manifolds in $$\mathbb {R}^4$$

IF 1.2 3区数学 Q1 MATHEMATICS

Research in the Mathematical Sciences Pub Date : 2024-05-18 DOI:10.1007/s40687-024-00450-1

A. C. Nabarro, M. C. Romero Fuster, M. C. Zanardo

引用次数: 0

Abstract

The parabolic subset of a 3-manifold generically immersed in $\mathbb {R}^4$ is a surface. We analyze in this study the generic geometrical behavior of such surface, considered as a submanifold of $\mathbb {R}^4$. Typical Singularity Theory techniques based on the analysis of the family of height functions are applied in order to describe the geometrical characterizations of different singularity types.

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$$\mathbb{R}^4$$中泛浸3-manifolds的抛物线子集几何学

一般浸没在 $\mathbb {R}^4$ 中的 3-manifold的抛物面子集是一个曲面。在本研究中，我们分析了作为 $\mathbb {R}^4$ 子曲面的这种曲面的一般几何行为。为了描述不同奇点类型的几何特征，我们应用了基于高度函数族分析的典型奇点理论技术。

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

Research in the Mathematical Sciences Mathematics-Computational Mathematics

CiteScore

2.00

自引率

8.30%

发文量

期刊介绍： Research in the Mathematical Sciences is an international, peer-reviewed hybrid journal covering the full scope of Theoretical Mathematics, Applied Mathematics, and Theoretical Computer Science. The Mission of the Journal is to publish high-quality original articles that make a significant contribution to the research areas of both theoretical and applied mathematics and theoretical computer science. This journal is an efficient enterprise where the editors play a central role in soliciting the best research papers, and where editorial decisions are reached in a timely fashion. Research in the Mathematical Sciences does not have a length restriction and encourages the submission of longer articles in which more complex and detailed analysis and proofing of theorems is required. It also publishes shorter research communications (Letters) covering nascent research in some of the hottest areas of mathematical research. This journal will publish the highest quality papers in all of the traditional areas of applied and theoretical areas of mathematics and computer science, and it will actively seek to publish seminal papers in the most emerging and interdisciplinary areas in all of the mathematical sciences. Research in the Mathematical Sciences wishes to lead the way by promoting the highest quality research of this type.