Twistor transforms of quaternionic functions and orthogonal complex   structures
  The theory of slice regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains \Omega\ of R^4. When \Omega\ is a symmetric slice domain, the twistor transform of such a function is a holomorphic curve in the Klein quadric. The case in which \Omega\ is the complement of a parabola is studied in detail and described by a rational quartic surface in the twistor space CP^3. 
Graziano Gentili, Simon Salamon, Caterina Stoppato
math.DG math.AG math.CV