Einstein-Weyl spaces and (1,n)-curves in the quadric surface
type: Item
instance of: scholarly article
title: Einstein-Weyl spaces and (1,n)-curves in the quadric surface
zbMATH Open document ID: 0593.53031
DOI: 10.1007/BF00132254
author: Henrik Pedersen
published in: Annals of Global Analysis and Geometry
publication date: 1986-01-01T00:00:00Z
review text: Following the ideas of Hitchin in the twistorial approach to 3- dimensional Einstein-Weyl geometry we construct a series of complex surfaces containing rational curves with self-intersection number 2. These mini twistor spaces are obtained by taking an n-fold covering of a neighbourhood of a (1,n)-curve in the quadric \({\mathbb{C}}{\mathbb{P}}_ 1\times {\mathbb{C}}{\mathbb{P}}_ 1\) branched along the curve. We describe the corresponding Einstein-Weyl geometry on the parameter space of curves.
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 32L25
Mathematics Subject Classification ID: 14H15
Mathematics Subject Classification ID: 32Q99
Mathematics Subject Classification ID: 53A30
zbMATH DE Number: 3953739
zbMATH Keywords: branched covering
zbMATH Keywords: conformal structure
zbMATH Keywords: geodesics
zbMATH Keywords: compatible
zbMATH Keywords: affine connection
zbMATH Keywords: Weyl space
zbMATH Keywords: Einstein-Weyl equation
zbMATH Keywords: Einstein-Weyl geometry
zbMATH Keywords: complex surfaces
zbMATH Keywords: rational curves
zbMATH Keywords: mini twistor spaces
zbMATH Keywords: n-fold covering
MaRDI profile type: Publication
cites work: Q4067705
cites work: Monopoles and geodesics
cites work: A theorem of completeness of characteristic systems for analytic families of compact submanifolds of complex manifolds
description: scientific article; zbMATH DE number 3953739