A characterization of Oeljeklaus-Toma manifolds in locally conformally Kähler geometry
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916619211505664 |
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| author | Kanda, Shuho |
| author_facet | Kanda, Shuho |
| contents | We show that for a certain class of solvable Lie groups, if they admit a left-invariant non-Vaisman locally conformally Kähler metric and a lattice, they must arise from the construction of Oeljeklaus-Toma manifolds. This result provides a natural explanation for why number-theoretic considerations play a role in the construction of Oeljeklaus-Toma manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12500 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A characterization of Oeljeklaus-Toma manifolds in locally conformally Kähler geometry Kanda, Shuho Differential Geometry Complex Variables We show that for a certain class of solvable Lie groups, if they admit a left-invariant non-Vaisman locally conformally Kähler metric and a lattice, they must arise from the construction of Oeljeklaus-Toma manifolds. This result provides a natural explanation for why number-theoretic considerations play a role in the construction of Oeljeklaus-Toma manifolds. |
| title | A characterization of Oeljeklaus-Toma manifolds in locally conformally Kähler geometry |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2502.12500 |