Fractional-linear integrals of geodesic flows on surfaces and Nakai's geodesic 4-webs

Sergey I. Agafonov; Thaís G. P. Alves

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arXiv · 2306.17540

Fractional-linear integrals of geodesic flows on surfaces and Nakai's geodesic 4-webs

Sergey I. Agafonov·Thaís G. P. Alves

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Abstract

We prove that if the geodesic flow on a surface has an integral, fractional-linear in momenta, then the dimension of the space of such integrals is either 3 or 5, the latter case corresponding to constant gaussian curvature. We give also a geometric criterion for existence of fractional-linear integrals: such integral exists if and only if the surface carries a geodesic 4-web with constant cross-ratio of the four directions tangent to the web leaves.

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BibTeX RIS

Sergey I. Agafonov, Thaís G. P. Alves. 2023-06-30. Fractional-linear integrals of geodesic flows on surfaces and Nakai's geodesic 4-webs. https://arxiv.org/abs/2306.17540

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