p-Kähler structures on compact complex manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916796017147904 |
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| author | Giudice, Ettore Lo |
| author_facet | Giudice, Ettore Lo |
| contents | Let $(M,J)$ be a complex manifold of complex dimension $n$. A $p$-Kähler structure on $(M,J)$ is a real, closed $(p,p)$-transverse form. In this paper, we address the conjecture of L. Alessandrini and G. Bassanelli on $(n-2)$-Kähler nilmanifolds equipped with nilpotent complex structures and holomorphically parallelizable nilmanifolds. We also derive necessary conditions for the existence of smooth curves of $p$-Kähler structures, starting from a fixed $p$-Kähler structure, along a differentiable family of compact complex manifolds. In addition, we study the cohomology classes of $p$-Kähler (resp. $p$-symplectic, $p$-pluriclosed) structures on compact complex manifolds. We provide several examples of families of compact complex manifolds admitting $p$-Kähler or $p$-symplectic structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13546 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | p-Kähler structures on compact complex manifolds Giudice, Ettore Lo Differential Geometry 32J27, 53C15, 32G05 Let $(M,J)$ be a complex manifold of complex dimension $n$. A $p$-Kähler structure on $(M,J)$ is a real, closed $(p,p)$-transverse form. In this paper, we address the conjecture of L. Alessandrini and G. Bassanelli on $(n-2)$-Kähler nilmanifolds equipped with nilpotent complex structures and holomorphically parallelizable nilmanifolds. We also derive necessary conditions for the existence of smooth curves of $p$-Kähler structures, starting from a fixed $p$-Kähler structure, along a differentiable family of compact complex manifolds. In addition, we study the cohomology classes of $p$-Kähler (resp. $p$-symplectic, $p$-pluriclosed) structures on compact complex manifolds. We provide several examples of families of compact complex manifolds admitting $p$-Kähler or $p$-symplectic structures. |
| title | p-Kähler structures on compact complex manifolds |
| topic | Differential Geometry 32J27, 53C15, 32G05 |
| url | https://arxiv.org/abs/2506.13546 |