Збережено в:
| Автор: | |
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| Формат: | Preprint |
| Опубліковано: |
2004
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| Предмети: | |
| Онлайн доступ: | https://arxiv.org/abs/math/0406225 |
| Теги: |
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Зміст:
- The geodesic flow of a Riemannian metric on a compact manifold $Q$ is said to be toric integrable if it is completely integrable and the first integrals of motion generate a homogeneous torus action on the punctured cotangent bundle $T^*Q\setminus{Q}$. If the geodesic flow is toric integrable, the cosphere bundle admits the structure of a contact toric manifold. By comparing the Betti numbers of contact toric manifolds and cosphere bundles, we are able to provide necessary conditions for the geodesic flow on a compact, connected 3-dimensional manifold to be toric integrable.