Rigidity of Lie foliations with locally symmetric leaves
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913855333990400 |
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| author | Meigniez, Gael Nozawa, Hiraku |
| author_facet | Meigniez, Gael Nozawa, Hiraku |
| contents | We prove that if the leaves of a minimal Lie foliation are locally isometric to a symmetric space of non-compact type without a Poincare disk factor, then the foliation is smoothly conjugate to a homogeneous Lie foliation up to finite covering. This result generalizes and strengthens Zimmer's theorem, which characterizes minimal Lie foliations with leaves isometric to a symmetric space of non-compact type without real rank one factors as pullbacks of homogeneous foliations. As applications, we extend Zimmer's arithmeticity theorem for holonomy groups and establish a rigidity theorem for Riemannian foliations with locally symmetric leaves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17633 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity of Lie foliations with locally symmetric leaves Meigniez, Gael Nozawa, Hiraku Differential Geometry Geometric Topology 57R30, 53C24, 37C85, 53C12 We prove that if the leaves of a minimal Lie foliation are locally isometric to a symmetric space of non-compact type without a Poincare disk factor, then the foliation is smoothly conjugate to a homogeneous Lie foliation up to finite covering. This result generalizes and strengthens Zimmer's theorem, which characterizes minimal Lie foliations with leaves isometric to a symmetric space of non-compact type without real rank one factors as pullbacks of homogeneous foliations. As applications, we extend Zimmer's arithmeticity theorem for holonomy groups and establish a rigidity theorem for Riemannian foliations with locally symmetric leaves. |
| title | Rigidity of Lie foliations with locally symmetric leaves |
| topic | Differential Geometry Geometric Topology 57R30, 53C24, 37C85, 53C12 |
| url | https://arxiv.org/abs/2505.17633 |