A Lagrangian approach to extremal curves on Stiefel manifolds

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.3934/jgm.2020031

K. Hüper, I. Markina, F. Leite

引用次数: 11

Abstract

A unified framework for studying extremal curves on real Stiefel manifolds is presented. We start with a smooth one-parameter family of pseudo-Riemannian metrics on a product of orthogonal groups acting transitively on Stiefel manifolds. In the next step Euler-Langrange equations for a whole class of extremal curves on Stiefel manifolds are derived. This includes not only geodesics with respect to different Riemannian metrics, but so-called quasi-geodesics and smooth curves of constant geodesic curvature, as well. It is shown that they all can be written in closed form. Our results are put into perspective to recent related work where a Hamiltonian rather than a Lagrangian approach was used. For some specific values of the parameter we recover certain well-known results.

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Stiefel流形上极值曲线的拉格朗日方法

给出了研究实Stiefel流形极值曲线的统一框架。我们从Stiefel流形上传递作用的正交群积上的光滑单参数伪黎曼度量族开始。其次，导出了Stiefel流形上一类极值曲线的欧拉-朗朗日方程。这不仅包括关于不同黎曼度量的测地线，还包括所谓的准测地线和恒定测地线曲率的光滑曲线。结果表明，它们都可以写成封闭形式。我们的结果与最近使用哈密顿方法而不是拉格朗日方法的相关工作相结合。对于某些特定的参数值，我们恢复了某些众所周知的结果。

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.