双曲面中角环演化的对偶性和几何学

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-29 DOI:10.1007/s40687-024-00434-1

Liang Chen, Shyuichi Izumiya, Masatomo Takahashi

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引用次数: 0

摘要

我们从对偶性的角度研究双曲面中光滑曲线的一种特殊演化（即所谓的角环演化）的几何性质。为此，我们首先回顾了第一位和第三位作者利用第二位作者提出的基本 Legendrian 对偶定理在双曲面中提出的（空间相似）正面的基本概念。此外，还定义了两种双曲循环演化，并研究了这两种不同演化之间的关系。研究结果表明，这两种演化相互之间具有 Legendrian 对偶性。

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Duality and geometry of horocyclic evolutes in hyperbolic plane

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Duality and geometry of horocyclic evolutes in hyperbolic plane

We investigate geometric properties of a special kind of evolutes, so-called horocyclic evolutes, of smooth curves in hyperbolic plane from the viewpoint of duality. To do that, we first review the basic notions of (spacelike) frontals in hyperbolic plane, which developed by the first and the third authors by using basic Legendrian duality theorem developed by the second author. Moreover, two kinds of horocyclic evolutes are defined and the relationship between these two different evolutes are studied. As results, they are Legendrian dual to each other.

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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.