On the Classification of Non-Homogeneous Solvable Lie Foliations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914450310692864 |
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| author | Ndiaye, Ameth |
| author_facet | Ndiaye, Ameth |
| contents | We study Lie foliations on compact manifolds whose transverse group is \emph{metabelian} (a natural generalization of the affine group $\GA$ considered in earlier work). We establish a complete classification of $\GA$-Lie foliations in dimension $5$, completing the work initiated in Dathe--Ndiaye. We then extend this analysis to foliations whose transverse group is a non-split metabelian Lie group, proving the existence of non-homogeneous Lie foliations with such groups in the smallest possible dimension. We introduce a new obstruction to homogeneity via the group cohomology $H^{2}(Γ,\mathbb{Z})$ of the holonomy group, and give exotic examples showing that non-polycyclicity of holonomy is not the only obstruction to homogeneity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04965 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Classification of Non-Homogeneous Solvable Lie Foliations Ndiaye, Ameth Dynamical Systems We study Lie foliations on compact manifolds whose transverse group is \emph{metabelian} (a natural generalization of the affine group $\GA$ considered in earlier work). We establish a complete classification of $\GA$-Lie foliations in dimension $5$, completing the work initiated in Dathe--Ndiaye. We then extend this analysis to foliations whose transverse group is a non-split metabelian Lie group, proving the existence of non-homogeneous Lie foliations with such groups in the smallest possible dimension. We introduce a new obstruction to homogeneity via the group cohomology $H^{2}(Γ,\mathbb{Z})$ of the holonomy group, and give exotic examples showing that non-polycyclicity of holonomy is not the only obstruction to homogeneity. |
| title | On the Classification of Non-Homogeneous Solvable Lie Foliations |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2604.04965 |