The Einstein-Weyl spaces associated to Segre quartic surfaces

Nobuhiro Honda; Fuminori Nakata

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arXiv · 2208.13567

The Einstein-Weyl spaces associated to Segre quartic surfaces

Nobuhiro Honda·Fuminori Nakata

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Abstract

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.

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BibTeX RIS

Nobuhiro Honda, Fuminori Nakata. 2022-08-29. The Einstein-Weyl spaces associated to Segre quartic surfaces. https://arxiv.org/abs/2208.13567

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