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Twistor transforms of quaternionic functions and orthogonal complex structures

Graziano GentiliSimon SalamonCaterina Stoppato — 2014

Journal of the European Mathematical Society

The theory of slice-regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains Ω of 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 P 3 .

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