The holonomy of spherically symmetric projective Finsler metrics of constant curvature
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913348026630144 |
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| author | Mezrag, Asma Muzsnay, Zoltan |
| author_facet | Mezrag, Asma Muzsnay, Zoltan |
| contents | In this paper, we investigate the holonomy group of $n$-dimensional projective Finsler metrics of constant curvature. We establish that in the spherically symmetric case, the holonomy group is maximal, and for a simply connected manifold it is isomorphic to $Diff_o({\mathbb S^{n-1}})$, the connected component of the identity of the group of smooth diffeomorphism on the $(n-1)$-dimensional sphere. In particular, the holonomy group of the n-dimensional standard Funk metric and the Bryant-Shen metrics are maximal and isomorphic to $Diff_o({\mathbb S^{n-1}})$. These results are the firsts describing explicitly the holonomy group of n-dimensional Finsler manifolds in the non-Berwaldian (that is when the canonical connection is non-linear) case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07563 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The holonomy of spherically symmetric projective Finsler metrics of constant curvature Mezrag, Asma Muzsnay, Zoltan Differential Geometry 53C29, 53B40, 22E65 In this paper, we investigate the holonomy group of $n$-dimensional projective Finsler metrics of constant curvature. We establish that in the spherically symmetric case, the holonomy group is maximal, and for a simply connected manifold it is isomorphic to $Diff_o({\mathbb S^{n-1}})$, the connected component of the identity of the group of smooth diffeomorphism on the $(n-1)$-dimensional sphere. In particular, the holonomy group of the n-dimensional standard Funk metric and the Bryant-Shen metrics are maximal and isomorphic to $Diff_o({\mathbb S^{n-1}})$. These results are the firsts describing explicitly the holonomy group of n-dimensional Finsler manifolds in the non-Berwaldian (that is when the canonical connection is non-linear) case. |
| title | The holonomy of spherically symmetric projective Finsler metrics of constant curvature |
| topic | Differential Geometry 53C29, 53B40, 22E65 |
| url | https://arxiv.org/abs/2405.07563 |