Self-dual Zollfrei conformal structures with [formula omitted]-surface foliation

Abstract

A global twistor correspondence is established for neutral self-dual conformal structures with α -surface foliation when the structure is close to the standard structure on S 2 × S 2 . We need to introduce some singularity for the α -surface foliation such that the leaves intersect on a fixed 2-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 local general forms of neutral self-dual metrics with α -surface foliation.