Compatible Complex Structures on Twistor Spaces

2008/10/07 by Guillaume Deschamps, Deschamps, Guillaume · 1 citation
Mathematics · #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.CV #math.DG

paper · pdf · doi:10.48550/arxiv.0810.1135

23 pages

arxiv created 2008/10/07 · openalex publication_date 2008/10/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (M,g) be a Riemannian 4-manifold. The twistor space Z->M is a CP1-bundle whose total space Z admits a natural metric h. The aim of this article is to study properties of complex structures on (Z,h) which are compatible with the CP1-fibration and the metric h. The results obtained enable us to translate some metric properties on M in terms of complex properties on its twistor space Z.

Cited by

• The Yang-Mills String as the A-Model on the Twistor Space of the Complex Two-Dimensional Projective Space with Fluxes and Wilson Loops: the Beta Function

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