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.
Twistor transforms of quaternionic functions and orthogonal complex structures / Gentili, Graziano; Salamon, Simon; Stoppato, Caterina. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - STAMPA. - 16:(2014), pp. 2323-2353. [10.4171/JEMS/488]
Twistor transforms of quaternionic functions and orthogonal complex structures
GENTILI, GRAZIANO;STOPPATO, CATERINA
2014
Abstract
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.
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