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Статья

Rational curves and special metrics on twistor spaces

Geometry and Topology. 2014. Vol. 18. No. 2. P. 897-909.

A Hermitian metric ω on a complex manifold is called SKT or pluriclosed if ddcω=0. Let M be a twistor space of a compact, anti-selfdual Riemannian manifold, admitting a pluriclosed Hermitian metric. We prove that in this case M is Kähler, hence isomorphic to CP3 or a flag space. This result is obtained from rational connectedness of the twistor space, due to F Campana. As an aside, we prove that the moduli space of rational curves on the twistor space of a K3 surface is Stein.