$\partial\bar{\partial}$-Lemma and $p$-Kähler structures on families of solvmanifolds
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929278129537024 |
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| author | Cattaneo, Andrea Tomassini, Adriano |
| author_facet | Cattaneo, Andrea Tomassini, Adriano |
| contents | We provide families of compact $(n + 1)$-dimensional complex non Kähler manifolds satisfying the $\partial\bar{\partial}$-Lemma, with holomoprhically trivial canonical bundle, carrying a balanced metric and with no $p$-Kähler structures. Such a construction extends to the completely solvable case in any dimension Nakamura's construction of low-dimensional holomorphically parallelizable solvmanifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10126 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\partial\bar{\partial}$-Lemma and $p$-Kähler structures on families of solvmanifolds Cattaneo, Andrea Tomassini, Adriano Differential Geometry 32J27, 57T15, 32Q99 We provide families of compact $(n + 1)$-dimensional complex non Kähler manifolds satisfying the $\partial\bar{\partial}$-Lemma, with holomoprhically trivial canonical bundle, carrying a balanced metric and with no $p$-Kähler structures. Such a construction extends to the completely solvable case in any dimension Nakamura's construction of low-dimensional holomorphically parallelizable solvmanifolds. |
| title | $\partial\bar{\partial}$-Lemma and $p$-Kähler structures on families of solvmanifolds |
| topic | Differential Geometry 32J27, 57T15, 32Q99 |
| url | https://arxiv.org/abs/2403.10126 |