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Abstract <p> 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. </p> <p> <b> DOI</b> 10.1134/S1061920824601836 </p>

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On Fractional-Linear Integrals of Geodesics on Surfaces

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • B. Kruglikov

摘要

Abstract

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