Compatible complex structures on twistor space
[Structures complexes compatibles sur les espace de twisteurs]
Deschamps, Guillaume
Annales de l'Institut Fourier, Tome 61 (2011), p. 2219-2248 / Harvested from Numdam
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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.

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.

Publié le : 2011-01-01
DOI : https://doi.org/10.5802/aif.2671
Classification:  53C28,  52C26
Mots clés: espace de twisteur, structure complexe, courbure scalaire nulle, Kähler à courbure scalaire nulle, localement conformément Kähler, quaternionique Kähler. 
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     title = {Compatible complex structures on twistor space},
     journal = {Annales de l'Institut Fourier},
     volume = {61},
     year = {2011},
     pages = {2219-2248},
     doi = {10.5802/aif.2671},
     zbl = {1267.53051},
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Deschamps, Guillaume. Compatible complex structures on twistor space. Annales de l'Institut Fourier, Tome 61 (2011) pp. 2219-2248. doi : 10.5802/aif.2671. http://gdmltest.u-ga.fr/item/AIF_2011__61_6_2219_0/

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