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 (6)

• Einstein-Weyl geometry, the dKP equation and twistor theory
• A class of Einstein--Weyl spaces associated to an integrable system of hydrodynamic type
• Anti-self-dual conformal structures with null Killing vectors from projective structures
• Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction
• Self-dual Zollfrei conformal structures with alpha-surface foliation
• Singular Self-dual Zollfrei Metrics and Twistor Correspondence

Cited by in corpus (7)

• Einstein--Weyl geometry, dispersionless Hirota equation and Veronese webs
• Integrable Background Geometries
• Kähler-Weyl manifolds of dimension 4
• Kaehler and para-Kaehler curvature Weyl manifolds
• The Einstein-Weyl Equations, Scattering Maps, and Holomorphic Disks
• Minitwistor spaces, Severi varieties, and Einstein-Weyl structure
• Wave equations and the LeBrun-Mason correspondence