The theory of slice-regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains of . When is a symmetric slice domain, the twistor transform of such a function is a holomorphic curve in the Klein quadric. The case in which is the complement of a parabola is studied in detail and described by a rational quartic surface in the twistor space .
Cite this article
Graziano Gentili, Simon Salamon, Caterina Stoppato, Twistor transforms of quaternionic functions and orthogonal complex structures. J. Eur. Math. Soc. 16 (2014), no. 11, pp. 2323–2353DOI 10.4171/JEMS/488