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

Bibliographic Details
Main Author: Agafonov, Sergey I. [UNESP]
Publication Date: 2024
Other Authors: Alves, Thaís G.P. [UNESP]
Format: Article
Language: eng
Source: Repositório Institucional da UNESP
Download full: http://dx.doi.org/10.1515/advgeom-2024-0008
https://hdl.handle.net/11449/307779
Summary: We prove that if the geodesic flow on a surface has an integral which is 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 the existence of fractional-linear integrals: such an 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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spelling Fractional-linear integrals of geodesic flows on surfaces and Nakai’s geodesic 4-websfractional-linear integralgeodesic 4-webgeodesic flowSurfaceWe prove that if the geodesic flow on a surface has an integral which is 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 the existence of fractional-linear integrals: such an 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.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Department of Mathematics São Paulo State University-UNESPDepartment of Mathematics São Paulo State University-UNESPFAPESP: #2022/12813-5CAPES: 88882.434346/2019-01Universidade Estadual Paulista (UNESP)Agafonov, Sergey I. [UNESP]Alves, Thaís G.P. [UNESP]2025-04-29T20:10:18Z2024-04-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article263-273http://dx.doi.org/10.1515/advgeom-2024-0008Advances in Geometry, v. 24, n. 2, p. 263-273, 2024.1615-71681615-715Xhttps://hdl.handle.net/11449/30777910.1515/advgeom-2024-00082-s2.0-85192189133Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengAdvances in Geometryinfo:eu-repo/semantics/openAccess2025-04-30T13:56:45Zoai:repositorio.unesp.br:11449/307779Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462025-04-30T13:56:45Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Fractional-linear integrals of geodesic flows on surfaces and Nakai’s geodesic 4-webs
title Fractional-linear integrals of geodesic flows on surfaces and Nakai’s geodesic 4-webs
spellingShingle Fractional-linear integrals of geodesic flows on surfaces and Nakai’s geodesic 4-webs
Agafonov, Sergey I. [UNESP]
fractional-linear integral
geodesic 4-web
geodesic flow
Surface
title_short Fractional-linear integrals of geodesic flows on surfaces and Nakai’s geodesic 4-webs
title_full Fractional-linear integrals of geodesic flows on surfaces and Nakai’s geodesic 4-webs
title_fullStr Fractional-linear integrals of geodesic flows on surfaces and Nakai’s geodesic 4-webs
title_full_unstemmed Fractional-linear integrals of geodesic flows on surfaces and Nakai’s geodesic 4-webs
title_sort Fractional-linear integrals of geodesic flows on surfaces and Nakai’s geodesic 4-webs
author Agafonov, Sergey I. [UNESP]
author_facet Agafonov, Sergey I. [UNESP]
Alves, Thaís G.P. [UNESP]
author_role author
author2 Alves, Thaís G.P. [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Agafonov, Sergey I. [UNESP]
Alves, Thaís G.P. [UNESP]
dc.subject.por.fl_str_mv fractional-linear integral
geodesic 4-web
geodesic flow
Surface
topic fractional-linear integral
geodesic 4-web
geodesic flow
Surface
description We prove that if the geodesic flow on a surface has an integral which is 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 the existence of fractional-linear integrals: such an 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.
publishDate 2024
dc.date.none.fl_str_mv 2024-04-01
2025-04-29T20:10:18Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1515/advgeom-2024-0008
Advances in Geometry, v. 24, n. 2, p. 263-273, 2024.
1615-7168
1615-715X
https://hdl.handle.net/11449/307779
10.1515/advgeom-2024-0008
2-s2.0-85192189133
url http://dx.doi.org/10.1515/advgeom-2024-0008
https://hdl.handle.net/11449/307779
identifier_str_mv Advances in Geometry, v. 24, n. 2, p. 263-273, 2024.
1615-7168
1615-715X
10.1515/advgeom-2024-0008
2-s2.0-85192189133
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Advances in Geometry
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 263-273
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv repositoriounesp@unesp.br
_version_ 1834482755263528960

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