Compatible complex structures on twistor space
Let be a Riemannian 4-manifold. The associated twistor space is a bundle whose total space admits a natural metric. The aim of this article is to study properties of complex structures on which are compatible with the fibration and the metric. The results obtained enable us to translate some metric properties on (scalar flat, scalar-flat Kähler...) in terms of complex properties of its twistor space .