A zoll counterexample to a geodesic length conjecture
We construct a counterexample to a conjectured inequality L ≤ 2D, relating the diameter D and the least length L of a nontrivial closed geodesic, for a Riemannian metric on the 2-sphere. The construction relies on Guillemin's theorem concerning the existence of Zoll surfaces integrating an arbi...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:287723 |
| Acceso en línea: | https://ddd.uab.cat/record/287723 https://dx.doi.org/urn:doi:10.1007/s00039-009-0708-9 |
| Access Level: | acceso abierto |
| Palabra clave: | Closed geodesic Diameter Guillemin deformation Sphere Systole Zoll surface |
| Sumario: | We construct a counterexample to a conjectured inequality L ≤ 2D, relating the diameter D and the least length L of a nontrivial closed geodesic, for a Riemannian metric on the 2-sphere. The construction relies on Guillemin's theorem concerning the existence of Zoll surfaces integrating an arbitrary infinitesimal odd deformation of the round metric. Thus the round metric is not optimal for the ratio L/D. |
|---|