Compatible complex structures on twistor space
Annales de l'Institut Fourier, Volume 61 (2011) no. 6, p. 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 : https://doi.org/10.5802/aif.2671
Classification:  53C28,  52C26
Keywords: twistor space, complex structure, scalar-flat, scalar-flat Kähler, locally conformally Kähler, quaternionic Kähler.
@article{AIF_2011__61_6_2219_0,
     author = {Deschamps, Guillaume},
     title = {Compatible complex structures on twistor space},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {61},
     number = {6},
     year = {2011},
     pages = {2219-2248},
     doi = {10.5802/aif.2671},
     mrnumber = {2976309},
     zbl = {1267.53051},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2011__61_6_2219_0}
}
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://www.numdam.org/item/AIF_2011__61_6_2219_0/

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