Twistor transforms of quaternionic functions and orthogonal complex structures

Abstract

The theory of slice regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains Ω of R^4. When Ω is a symmetric slice domain, the twistor transform of such a function is a holomorphic curve in the Klein quadric. The case in which Ω is the complement of a parabola is studied in detail and described by a rational quartic surface in the twistor space CP^3.

Some explanation added in section 1, other minor amendments and reformatting; to appear in JEMS