三维共形测地线的变分性

IF 1.6 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2025-09-02 DOI:10.1007/s13324-025-01124-z

Boris Kruglikov, Vladimir S. Matveev, Wijnand Steneker

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引用次数: 0

摘要

保形测地线在保形流形中形成了一个不变定义的非参数化曲线族，它推广了非参数化测地线/射影连接的路径。描述它们的方程是三阶的，它们是否由欧拉-拉格朗日方程给出是一个开放的问题。在第三维（最简单的，但从物理应用的角度来看最重要的），我们证明了非参数化共形测地线的方程是变分的。

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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Variationality of Conformal Geodesics in dimension 3

Conformal geodesics form an invariantly defined family of unparametrized curves in a conformal manifold generalizing unparametrized geodesics/paths of projective connections. The equation describing them is of third order, and it was an open problem whether they are given by an Euler–Lagrange equation. In dimension 3 (the simplest, but most important from the viewpoint of physical applications) we demonstrate that the equation for unparametrized conformal geodesics is variational.

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来源期刊

Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

0.00%

发文量

122

期刊介绍： Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.