Singularity properties of Lorentzian Darboux surfaces in Lorentz–Minkowski spacetime

IF 1.2 3区数学 Q1 MATHEMATICS

Research in the Mathematical Sciences Pub Date : 2024-01-30 DOI:10.1007/s40687-023-00420-z

Yanlin Li, Xuelian Jiang, Zhigang Wang

引用次数: 0

Abstract

In this paper, by virtue of unfolding theory in singularity theory, we investigate the singularities of five special surfaces generated by a regular curve lying on a spacelike hypersurface in Lorentz–Minkowski 4-space. Using two kinds of extended Lorentzian Darboux frames along the curve as tools, five new invariants are obtained to characterize the singularities of five special surfaces and their geometric meanings are discussed in detail. In addition, some dual relationships between a normal curve of the original curve and five surfaces are revealed under the meanings of Legendrian duality.

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洛伦兹-闵科夫斯基时空中洛伦兹达布曲面的奇异特性

本文借助奇点理论中的展开理论，研究了洛伦兹-闵科夫斯基 4 空间中一条位于空间相似超曲面上的规则曲线所产生的五个特殊曲面的奇点。以两种沿曲线扩展的洛伦兹达尔布框架为工具，我们得到了五个新的不变式来表征五个特殊曲面的奇点，并详细讨论了它们的几何意义。此外，在 Legendrian 对偶的意义下，还揭示了原曲线的法线与五个曲面之间的一些对偶关系。

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.