Gronwall's conjecture for 3-webs with two pencils of lines
We prove the old-standing Gronwall conjecture in the particular case of linear 3-webs whose 2 foliations are 2 pencils of lines. For a non-hexagonal 3-web, we also introduce a family of projective torsion-free Cartan connections, the web leaves being geodesics for each member of the family, and give...
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | Brasil |
| Recursos: | Universidade Estadual Paulista (UNESP) |
| Repositorio: | Repositório Institucional da UNESP |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unesp.br:11449/307427 |
| Acesso em linha: | http://dx.doi.org/10.1016/j.difgeo.2023.102071 https://hdl.handle.net/11449/307427 |
| Access Level: | acceso abierto |
| Palavra-chave: | Cartan connection Gronwall conjecture Linear 3-web |
| Resumo: | We prove the old-standing Gronwall conjecture in the particular case of linear 3-webs whose 2 foliations are 2 pencils of lines. For a non-hexagonal 3-web, we also introduce a family of projective torsion-free Cartan connections, the web leaves being geodesics for each member of the family, and give a web linearization criterion. |
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