Closed Geodesics on Weingarten Surfaces with [math]

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-03 DOI:10.1137/23m1608616

Frank E. Baginski, Valério Ramos Batista

引用次数: 0

Abstract

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 3, Page 1705-1719, September 2024.
Abstract.In 2006, Alexander proved a result that implies for a Weingarten surface [math], if [math] is the number of times a closed geodesic winds around the axis of rotation and [math] is the number of times the geodesic oscillates about the equator, then [math] when [math] and [math] when [math]. In this paper, we present another proof of Alexander’s result for the Weingarten surfaces [math] that is simpler and more direct. Our approach uses sharp estimates of certain improper integrals to obtain the intervals for permissible ratios [math]. We numerically compute a number of closed geodesics for various combinations of [math] to illustrate the variety of patterns that are possible.

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有[数学]的魏格登曲面上的闭合大地线

SIAM 应用动力系统期刊》，第 23 卷第 3 期，第 1705-1719 页，2024 年 9 月。摘要.2006 年，亚历山大证明了一个结果，即对于魏格登曲面[math]，如果[math]是闭合大地线绕旋转轴旋转的次数，[math]是大地线绕赤道摆动的次数，则当[math]为[math]时，[math]为[math]；当[math]为[math]时，[math]为[math]。在本文中，我们提出了亚历山大对魏格登曲面[math]结果的另一个证明，它更简单、更直接。我们的方法是利用某些不完全积分的尖锐估计来获得允许比率的区间[math]。我们用数值计算了[math]的各种组合的闭合大地线，以说明可能存在的各种模式。

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.