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

Abstract

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 $C{P}^1\times C{P}^1$ 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.

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

References in corpus (1)

• Self-dual Zollfrei conformal structures with alpha-surface foliation

Cited by in corpus (3)

• The Einstein-Weyl Equations, Scattering Maps, and Holomorphic Disks
• Wave equations and the LeBrun-Mason correspondence
• Minitwistor spaces, Severi varieties, and Einstein-Weyl structure