The Einstein-Weyl spaces associated to Segre quartic surfaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866915062020571136 |
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| author | Honda, Nobuhiro Nakata, Fuminori |
| author_facet | Honda, Nobuhiro Nakata, Fuminori |
| contents | We find explicit examples of compact minitwistor spaces of genus one, whose Einstein-Weyl spaces have a connected component that is diffeomorphic to the de Sitter space. The induced Einstein-Weyl structure on it is Lorenzian, real-analytic, whose spacelike geodesics are all closed and simple. The identity component of the automorphism group of the Einstein-Weyl structure is the circle and therefore the structure is not isomorphic to the standard de Sitter structure. We show that these Einstein-Weyl structures deform as the Segre surfaces deform and converge to the standard de Sitter structure.
The minitwistor spaces we study are the so-called Segre quartic surfaces. They have a real pair of nodes, which play a crucial role in proving the above results. These singularities also allow us to construct explicit examples of non-compact complex surfaces that do not admit any compactification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_13567 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Einstein-Weyl spaces associated to Segre quartic surfaces Honda, Nobuhiro Nakata, Fuminori Differential Geometry Algebraic Geometry We find explicit examples of compact minitwistor spaces of genus one, whose Einstein-Weyl spaces have a connected component that is diffeomorphic to the de Sitter space. The induced Einstein-Weyl structure on it is Lorenzian, real-analytic, whose spacelike geodesics are all closed and simple. The identity component of the automorphism group of the Einstein-Weyl structure is the circle and therefore the structure is not isomorphic to the standard de Sitter structure. We show that these Einstein-Weyl structures deform as the Segre surfaces deform and converge to the standard de Sitter structure. The minitwistor spaces we study are the so-called Segre quartic surfaces. They have a real pair of nodes, which play a crucial role in proving the above results. These singularities also allow us to construct explicit examples of non-compact complex surfaces that do not admit any compactification. |
| title | The Einstein-Weyl spaces associated to Segre quartic surfaces |
| topic | Differential Geometry Algebraic Geometry |
| url | https://arxiv.org/abs/2208.13567 |