JournalsjemsVol. 16, No. 11pp. 2323–2353

Twistor transforms of quaternionic functions and orthogonal complex structures

  • Graziano Gentili

    Università degli Studi di Firenze, Italy
  • Simon Salamon

    King's College London, UK
  • Caterina Stoppato

    Università di Firenze, Italy
Twistor transforms of quaternionic functions and orthogonal complex structures cover
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Abstract

The theory of slice-regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains Ω\Omega of R4\mathbb R^4. When Ω\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 Ω\Omega is the complement of a parabola is studied in detail and described by a rational quartic surface in the twistor space CP3\mathbb CP^3.

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. 2323–2353

DOI 10.4171/JEMS/488