Espaces twistoriels et structures complexes non standards.

Guillaume Deschamps (1)

1 IECN - Institut Élie Cartan de Nancy

In this paper we use the twistor theory in order to build non standard complex structures (with a meaning which we define) on products of 4-manifolds with the sphere of dimension two. To that end, we enumerate the set of complex surfaces whose twistor space is topologically trivial. Among these surfaces, we determine those which admit a spin structure or an anti-selfdual riemannian metric.

Mots clés: métrique anti-autoduale; Espace twistoriel; classification de Kodaira; structure spin; métrique anti-autoduale.

Domaines: Variables complexes [math.CV]

Guillaume Deschamps. Espaces twistoriels et structures complexes non standards.. 2006. ⟨hal-00021475⟩