洛伦兹-闵科夫斯基时空中洛伦兹达布曲面的奇异特性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-01-30 DOI:10.1007/s40687-023-00420-z

Yanlin Li, Xuelian Jiang, Zhigang Wang

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摘要

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。

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Singularity properties of Lorentzian Darboux surfaces in Lorentz–Minkowski spacetime

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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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.

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