Rigidity of flat holonomies
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866911969227833344 |
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| author | Besson, Gérard Courtois, Gilles Hersonsky, Sa'ar |
| author_facet | Besson, Gérard Courtois, Gilles Hersonsky, Sa'ar |
| contents | We prove that the existence of one horosphere in the universal cover of a closed, strictly quarter pinched, negatively curved Riemannian manifold of dimension $n\geq 3$ on which the stable holonomy along minimizing geodesics coincide with the Riemannian parallel transport, implies that the manifold is homothetic to a real hyperbolic manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_14136 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rigidity of flat holonomies Besson, Gérard Courtois, Gilles Hersonsky, Sa'ar Differential Geometry Dynamical Systems Primary: 58B20, Secondary: 57N16 We prove that the existence of one horosphere in the universal cover of a closed, strictly quarter pinched, negatively curved Riemannian manifold of dimension $n\geq 3$ on which the stable holonomy along minimizing geodesics coincide with the Riemannian parallel transport, implies that the manifold is homothetic to a real hyperbolic manifold. |
| title | Rigidity of flat holonomies |
| topic | Differential Geometry Dynamical Systems Primary: 58B20, Secondary: 57N16 |
| url | https://arxiv.org/abs/2308.14136 |