Uniformization of conformally flat hermitian surfaces
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.
scientific article; zbMATH DE number 118416
scientific article