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

Autor(es)

Agafonov, Sergey I. ; Alves, Thais G. P.

• Tipo de documento: Artigo Científico
• Fonte: ADVANCES IN GEOMETRY; v. 24, n. 2, p. 11-pg., 2024-04-25.

Resumo

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. (AU)

• Processo FAPESP: 22/12813-5 - Webs de posto positivo com geometria prescrita
• Beneficiário: Serguei Agafonov
• Modalidade de apoio: Auxílio à Pesquisa - Regular