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

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
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