On fractional-linear integrals of geodesics on surfaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929643221680128 |
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| author | Kruglikov, Boris |
| author_facet | Kruglikov, Boris |
| contents | 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 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 will also consider explicit examples and discuss a relation of such rational integrals to Killing vectors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04907 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On fractional-linear integrals of geodesics on surfaces Kruglikov, Boris Differential Geometry Mathematical Physics 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 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 will also consider explicit examples and discuss a relation of such rational integrals to Killing vectors. |
| title | On fractional-linear integrals of geodesics on surfaces |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2412.04907 |