1. Compatible Complex Structures on Twistor Spaces
- Author
-
Deschamps, Guillaume, Laboratoire de mathématiques de Brest (LM), Université de Brest (UBO)-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS), and Deschamps, Guillaume
- Subjects
Mathematics - Differential Geometry ,Differential Geometry (math.DG) ,Mathematics - Complex Variables ,[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] ,FOS: Mathematics ,[MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV] ,[MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV] ,Mathematics::Differential Geometry ,Complex Variables (math.CV) ,[MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG] - 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., 23 pages
- Published
- 2009