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arXiv · 2412.04907

On fractional-linear integrals of geodesics on surfaces

Boris Kruglikov
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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 M\"obius transformations the moduli space of such local integrals (if nonempty) is either the two-dimensional projective plane or a finite number of points. We will also consider explicit examples and discuss a relation of such rational integrals to Killing vectors.

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Boris Kruglikov. 2024-12-06. On fractional-linear integrals of geodesics on surfaces. https://arxiv.org/abs/2412.04907

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