Special Hermitian structures on suspensions
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908542986878976 |
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| author | Fino, Anna Grantcharov, Gueo Verbitsky, Misha |
| author_facet | Fino, Anna Grantcharov, Gueo Verbitsky, Misha |
| contents | Motivated by the construction based on topological suspension of a family of compact non-Kähler complex manifolds with trivial canonical bundle given by L. Qin and B. Wang in [QW], we study toric suspensions of balanced manifolds by holomorphic automorphisms. In particular, we show that toric suspensions of Calabi-Yau manifolds are balanced. We also prove that suspensions associated with hyperbolic automorphisms of hyperkähler manifolds do not admit any pluriclosed, astheno-Kähler or p-pluriclosed Hermitian metric. Moreover, we consider natural extensions for hypercomplex manifolds, providing some explicit examples of compact holomorphic symplectic and hypercomplex non-Kähler manifolds. We also show that a modified suspension construction provides examples with pluriclosed metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_12168 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Special Hermitian structures on suspensions Fino, Anna Grantcharov, Gueo Verbitsky, Misha Differential Geometry Motivated by the construction based on topological suspension of a family of compact non-Kähler complex manifolds with trivial canonical bundle given by L. Qin and B. Wang in [QW], we study toric suspensions of balanced manifolds by holomorphic automorphisms. In particular, we show that toric suspensions of Calabi-Yau manifolds are balanced. We also prove that suspensions associated with hyperbolic automorphisms of hyperkähler manifolds do not admit any pluriclosed, astheno-Kähler or p-pluriclosed Hermitian metric. Moreover, we consider natural extensions for hypercomplex manifolds, providing some explicit examples of compact holomorphic symplectic and hypercomplex non-Kähler manifolds. We also show that a modified suspension construction provides examples with pluriclosed metrics. |
| title | Special Hermitian structures on suspensions |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2208.12168 |