Twistor spaces and non-standard complex structures. (Espaces twistoriels et structures complexes non standards.) (French. English summary) Zbl 1202.53050

Deschamps, Guillaume

Publ. Mat., Barc. 52, No. 2, 435-457 (2008).

Summary: We use the twistor theory in order to build “non standard” complex structures (with a meaning which we define) on the products of 4-manifolds with the sphere of dimension two. To that end, we enumerate the set of complex surfaces whose twistor space is \({\mathcal C}^\infty\)-trivial. Among these surfaces will study those which admit an anti-self-cual Riemannian metric.

MSC:

53C28	Twistor methods in differential geometry
51M99	Real and complex geometry
53C27	Spin and Spin\({}^c\) geometry

Keywords:

complex surfaces; anti-self-cual Riemannian metric