Uniformization of conformally flat hermitian surfaces
type: Item
instance of: scholarly article
title: Uniformization of conformally flat hermitian surfaces
zbMATH Open document ID: 0766.53052
DOI: 10.1016/0926-2245(92)90016-G
author: Massimiliano Pontecorvo
published in: Differential Geometry and its Applications
publication date: 1993-02-10T00:00:00Z
review text: In this note the author considers a compact complex surface \(M\) with a conformally flat hermitian metric \(g\) which means that the complex structure \(J\) is an isometry: \(g(JX,JY)=g(X,Y)\) for any tangent vectors \(X\), \(Y\) on \(M\). Using the methods of twistor geometry the author classifies these surfaces. This is accomplished by first associating to the universal covering of such a surface an open set of a quadric in \(\mathbb{C}\mathbb{P}_ 3\) (the twistor space of \(S^ 4\)) and then applying some classical projective geometry.
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 32L25
zbMATH DE Number: 118416
zbMATH Keywords: Möbius transformation
zbMATH Keywords: twistor geometry
zbMATH Keywords: twistor space
Wikidata QID: Q115362746
reviewed by: Neda Bokan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 118416