A construction of Einstein-Weyl spaces via LeBrun-Mason type twistor correspondence

Details A construction of Einstein-Weyl spaces via LeBrun-Mason type twistor correspondence A construction of Einstein-Weyl spaces via LeBrun-Mason type twistor correspondence

2008-06-17

arxiv.org/abs/0806.2696v2

Mathematics

Differential Geometry

34pages; definition 1.5 added, proof of Lemma 7.2 replaced

Scientific paper

10.1007/s00220-009-0750-3

We construct infinitely many Einstein-Weyl structures on $S^2 \times R$ of signature (-++) which is sufficiently close to the model case of constant curvature, and whose space-like geodesics are all closed. Such structures are obtained from small perturbations of the diagonal of $CP^1 \times CP^1$ using the method of LeBrun-Mason type twistor theory. The geometry of constructed Einstein-Weyl space is well understood from the configuration of holomorphic disks. We also review Einstein-Weyl structures and their properties in the former half of this article.

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