Twistor transforms of quaternionic functions and orthogonal complex structures
Differential Geometry
2015-07-27 v2 Algebraic Geometry
Complex Variables
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.
Cite
@article{arxiv.1205.3513,
title = {Twistor transforms of quaternionic functions and orthogonal complex structures},
author = {Graziano Gentili and Simon Salamon and Caterina Stoppato},
journal= {arXiv preprint arXiv:1205.3513},
year = {2015}
}
Comments
Some explanation added in section 1, other minor amendments and reformatting; to appear in JEMS