Bounded distance geodesic foliations in Riemannian planes
A conjecture of Burns and Knieper (1991) asks whether a 2-plane with a metric without conjugate points, and with a geodesic foliation whose lines are at bounded Hausdorff distance, is necessarily flat. We prove this conjecture in two cases: under the hypothesis that the plane admits total curvature,...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad Autónoma de Madrid |
| Repositorio: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.uam.es:10486/741820 |
| Acceso en línea: | https://hdl.handle.net/10486/741820 https://dx.doi.org/10.1515/crelle-2023-0023 |
| Access Level: | acceso abierto |
| Palabra clave: | Riemaannian plane geodesic foliation conjugate points Burns-Knieper conjeture Matemáticas |
| Sumario: | A conjecture of Burns and Knieper (1991) asks whether a 2-plane with a metric without conjugate points, and with a geodesic foliation whose lines are at bounded Hausdorff distance, is necessarily flat. We prove this conjecture in two cases: under the hypothesis that the plane admits total curvature, and under the hypothesis of visibility at some point. Along the way, we show that all geodesic line foliations on a Riemannian 2-plane must be homeomorphic to the standard one |
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