Compatible complex structures on twistor space
Annales de l'Institut Fourier, Volume 61 (2011) no. 6, pp. 2219-2248.

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

Soit M une 4-variété riemannienne. L’espace de twisteur associé est un fibré qui admet une métrique naturelle. Le but de cet article est d’étudier les structures complexes sur Z qui sont compatibles avec la fibration et la métrique. Les résultats obtenu permettent d’exprimer des propriétés métriques sur M (courbure scalaire nulle, Kähler à courbure scalaire nulle...) en termes de propriétés des structures complexes de l’espace de twisteur Z.

DOI: 10.5802/aif.2671
Classification: 53C28,  52C26
Keywords: twistor space, complex structure, scalar-flat, scalar-flat Kähler, locally conformally Kähler, quaternionic Kähler.
Deschamps, Guillaume 1

1 Laboratoire de mathematiques de Brest UMR 6205 6 avenue de Gorgeu 29238 Brest cedex 3 France
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Deschamps, Guillaume. Compatible complex structures on twistor space. Annales de l'Institut Fourier, Volume 61 (2011) no. 6, pp. 2219-2248. doi : 10.5802/aif.2671. http://archive.numdam.org/articles/10.5802/aif.2671/

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