K-contact manifolds with minimal closed Reeb orbits
Fuente:
arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912384452395008 |
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| author | Li, Hui |
| author_facet | Li, Hui |
| contents | We use the Boothby-Wang fibration to construct certain simply connected K-contact manifolds and we give sufficient and necessary conditions on when such K-contact manifolds are homeomorphic to the odd dimensional spheres. If the symplectic base manifold of the fibration admits a Hamiltonian torus action, we show that on the total space of the fibration, other than the regular K-contact structures which have infinitely many closed Reeb orbits, there are K-contact structures whose closed Reeb orbits correspond exactly to the fixed points of the Hamiltonian torus action on the base manifold. Then we give a collection of examples of compact simply connected K-contact manifolds with minimal number of closed Reeb orbits which are not homeomorphic to the odd dimensional spheres, while having the real cohomology ring of the spheres. Finally, we give a family of examples of simply connected K-contact manifolds which have one more than the minimal number of closed Reeb orbits and which do not have the real cohomology ring of the spheres. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_10866 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | K-contact manifolds with minimal closed Reeb orbits Li, Hui Symplectic Geometry Differential Geometry Primary: 53D10, 53D05, 53D20, Secondary: 55N10, 57R20 We use the Boothby-Wang fibration to construct certain simply connected K-contact manifolds and we give sufficient and necessary conditions on when such K-contact manifolds are homeomorphic to the odd dimensional spheres. If the symplectic base manifold of the fibration admits a Hamiltonian torus action, we show that on the total space of the fibration, other than the regular K-contact structures which have infinitely many closed Reeb orbits, there are K-contact structures whose closed Reeb orbits correspond exactly to the fixed points of the Hamiltonian torus action on the base manifold. Then we give a collection of examples of compact simply connected K-contact manifolds with minimal number of closed Reeb orbits which are not homeomorphic to the odd dimensional spheres, while having the real cohomology ring of the spheres. Finally, we give a family of examples of simply connected K-contact manifolds which have one more than the minimal number of closed Reeb orbits and which do not have the real cohomology ring of the spheres. |
| title | K-contact manifolds with minimal closed Reeb orbits |
| topic | Symplectic Geometry Differential Geometry Primary: 53D10, 53D05, 53D20, Secondary: 55N10, 57R20 |
| url | https://arxiv.org/abs/2406.10866 |