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Complex Structures and Conformal Geometry

Simon Salamon — 2009

Bollettino dell'Unione Matematica Italiana

A characterization of certain complex structures on conformally-flat domains in real dimension 4 is carried out in the context of Hermitian geometry and twistor spaces. The presentation is motivated by some classical surface theory, whilst the problem itself leads to a refined classification of quadrics in complex projective 3-space. The main results are sandwiched between general facts in real dimension 2n and some concluding examples in real dimension 6.

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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