Gray-Hervella classes on product twistor spaces
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911593031270400 |
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| author | Davidov, Johann |
| author_facet | Davidov, Johann |
| contents | Motivated by generalized geometry (in the sense of Hitchin), the product bundle ${\mathcal Z}\times_{M} {\mathcal Z}$ of the twistor space ${\mathcal Z}$ of a Riemannian manifold $(M,g)$ is considered. The product twistor space admits a natural family of Riemannian metrics and four compatible almost complex structures, analogs of the Atiyah-Hitchin-Singer and Eells-Salamon almost complex structures on the twistor space. The Gray-Hervellal classes of these almost Hermitian structures are determined in the case when the dimension of the base manifold $M$ is four. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_12849 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gray-Hervella classes on product twistor spaces Davidov, Johann Differential Geometry 53C28, 53C55, 53C15 Motivated by generalized geometry (in the sense of Hitchin), the product bundle ${\mathcal Z}\times_{M} {\mathcal Z}$ of the twistor space ${\mathcal Z}$ of a Riemannian manifold $(M,g)$ is considered. The product twistor space admits a natural family of Riemannian metrics and four compatible almost complex structures, analogs of the Atiyah-Hitchin-Singer and Eells-Salamon almost complex structures on the twistor space. The Gray-Hervellal classes of these almost Hermitian structures are determined in the case when the dimension of the base manifold $M$ is four. |
| title | Gray-Hervella classes on product twistor spaces |
| topic | Differential Geometry 53C28, 53C55, 53C15 |
| url | https://arxiv.org/abs/2604.12849 |