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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.05702 |
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| _version_ | 1866916916886503424 |
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| author | Bieliavsky, Pierre Willaert, Maxime |
| author_facet | Bieliavsky, Pierre Willaert, Maxime |
| contents | Answering a conjecture by S. Kobayashi, in 1986, K. Sekigawa and L. Vanhecke proved that an almost hermitian manifold whose local geodesic symmetries preserve the Kähler 2-form is a locally symmetric hermitian space.
In the present paper, we relax the hermitean hypothesis by only requiring the manifold to be symplectic. In other words, we study the symplectic manifolds equipped with a symplectic connection whose geodesic symmetries are (local) symplectomorphisms. We call ``S-type'' these affine symplectic manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05702 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symplectic structures preserved by geodesic symmetries Bieliavsky, Pierre Willaert, Maxime Symplectic Geometry Answering a conjecture by S. Kobayashi, in 1986, K. Sekigawa and L. Vanhecke proved that an almost hermitian manifold whose local geodesic symmetries preserve the Kähler 2-form is a locally symmetric hermitian space. In the present paper, we relax the hermitean hypothesis by only requiring the manifold to be symplectic. In other words, we study the symplectic manifolds equipped with a symplectic connection whose geodesic symmetries are (local) symplectomorphisms. We call ``S-type'' these affine symplectic manifolds. |
| title | Symplectic structures preserved by geodesic symmetries |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2411.05702 |