PROJECTIVELY FLAT SURFACES AND BOGOMOLOV'S THEOREM ON CLASS <font>VII</font>₀ SURFACES

Abstract

We give a complete proof of Bogomolov's theorem on class VII 0 surfaces starting with the idea of Li, Yau and Zheng to use Kobayashi-Hitchin correspondence. We show that, because of the non-topological character of Gauduchon's degree, the proof of these authors is not complete. We prove that any projectively flat hermitian surface is locally conformally flat-Kähler, which reduces the problem to the classification of locally conformally flat-Kähler surfaces.