Compatible complex structures on twistor space
نویسنده
چکیده
— 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. Résumé. — 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, g) be a Riemannian 4-manifold. The twistor space Z → M is a CP 1-bundle whose total space Z admits a natural metric g̃. The aim of this article is to study properties of complex structures on (Z, g̃) which are compatible with the CP 1-fibration and the metric g̃. The results obtained enable us to translate some metric properties on M in terms of complex properties on its twistor space Z.
منابع مشابه
Compatible Complex Structures on Twistor Spaces
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