On a Modification of the Twistor Space

Abstract

In the paper we construct a modification $S(M)$ of the twistor space of a K\"ahler scalar flat surface $M$ and study its complex-geometric and metric properties. In particular, we construct complete balanced metrics on $S(M)$ and show that $S(M)$ can not be K\"ahler when $M$ is a compact simple hyperk\"ahler manifold.