Symmetric and skew-symmetric complex structures
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912291058876416 |
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| author | Bazzoni, Giovanni Gil-García, Alejandro Latorre, Adela |
| author_facet | Bazzoni, Giovanni Gil-García, Alejandro Latorre, Adela |
| contents | On a complex manifold $(M,J)$, we interpret complex symplectic and pseudo-Kähler structures as symplectic forms with respect to which $J$ is, respectively, symmetric and skew-symmetric. We classify complex symplectic structures on 4-dimensional Lie algebras. We develop a method for constructing hypersymplectic structures from the above data. This allows us to obtain an example of a hypersymplectic structure on a 4-step nilmanifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_11953 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Symmetric and skew-symmetric complex structures Bazzoni, Giovanni Gil-García, Alejandro Latorre, Adela Differential Geometry High Energy Physics - Theory Symplectic Geometry 57N16 (Primary) 22E25, 53C25, 53D05 (Secondary) On a complex manifold $(M,J)$, we interpret complex symplectic and pseudo-Kähler structures as symplectic forms with respect to which $J$ is, respectively, symmetric and skew-symmetric. We classify complex symplectic structures on 4-dimensional Lie algebras. We develop a method for constructing hypersymplectic structures from the above data. This allows us to obtain an example of a hypersymplectic structure on a 4-step nilmanifold. |
| title | Symmetric and skew-symmetric complex structures |
| topic | Differential Geometry High Energy Physics - Theory Symplectic Geometry 57N16 (Primary) 22E25, 53C25, 53D05 (Secondary) |
| url | https://arxiv.org/abs/2101.11953 |