On a Modification of the Twistor Space

In the paper we construct a modification $S(M)$ of the twistor space of a Kähler 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 Kähler when $M$ is a compact simple hyperkähler manifold.

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