Self-dual Zollfrei conformal structures with alpha-surface foliation

Abstract

A global twistor correspondence is established for neutral self-dual conformal structures with alpha-surface foliation when the structure is close to the standard structure on S^2 times S^2. We need to introduce some singularity for the alpha-surface foliation such that the leaves intersect on a fixed two sphere. In this correspondence, we prove that a natural double fibration is induced on some quotient spaces which is equal to the standard double fibration for the standard Zoll projective structure. We also give a local general forms of neutral self-dual metrics with alpha-surface foliation.

35pages

References in corpus (4)

• Anti-self-dual four-manifolds with a parallel real spinor
• Anti-self-dual conformal structures with null Killing vectors from projective structures
• Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction
• Singular Self-dual Zollfrei Metrics and Twistor Correspondence

Cited by in corpus (5)

• Integrable Background Geometries
• Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction
• A construction of Einstein-Weyl spaces via LeBrun-Mason type twistor correspondence
• Gauge theory on projective surfaces and anti-self-dual Einstein metrics in dimension four
• Wave equations and the LeBrun-Mason correspondence