Salamon: Complex Structures and Conformal Geometry

Salamon, Simon:
Complex Structures and Conformal Geometry
Bollettino dell'Unione Matematica Italiana Serie 9 2 (2009), fasc. n.1, p. 199-224, (English)
pdf (2.52 MB), djvu (320 Kb). | MR 2493651 | Zbl 1182.53043

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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.

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