3-Manifolds admitting toric integrable geodesic flows
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2004
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918132713521152 |
|---|---|
| author | Lee, Christopher R. |
| author_facet | Lee, Christopher R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0406225 |
| institution | arXiv |
| publishDate | 2004 |
| record_format | arxiv |
| spellingShingle | 3-Manifolds admitting toric integrable geodesic flows Lee, Christopher R. Differential Geometry Symplectic Geometry 53D25, 53D10 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. |
| title | 3-Manifolds admitting toric integrable geodesic flows |
| topic | Differential Geometry Symplectic Geometry 53D25, 53D10 |
| url | https://arxiv.org/abs/math/0406225 |