曲面上测地线的分数-线性积分

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI:10.1134/S1061920824601836

B. Kruglikov

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引用次数: 0

摘要

在本文中，我们给出了黎曼曲面上测地流的分数线性积分存在的一个判据，并解释了，对Möbius变换取模，这种局部积分的模空间（如果是非空的）要么是二维投影平面，要么是有限个数的点。我们还考虑了显式的例子，并讨论了这种有理积分与杀戮向量的关系。DOI 10.1134 / S1061920824601836

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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On Fractional-Linear Integrals of Geodesics on Surfaces

In this note, we give a criterion for the existence of a fractional-linear integral for a geodesic flow on a Riemannian surface and explain that, modulo the Möbius transformations, the moduli space of such local integrals (if nonempty) is either the two-dimensional projective plane or a finite number of points. We also consider explicit examples and discuss a relation of such rational integrals to Killing vectors.

DOI 10.1134/S1061920824601836

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.