Rational curves and special metrics on twistor spaces

Abstract

A Hermitian metric $\omega$ on a complex manifold is called SKT or pluriclosed if $d{d}^c\omega =0$. 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 $\C P^3$ 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.

12 pages

References in corpus (2)

• Autour de la cohomologie de Bott-Chern
• Pseudoholomorphic curves on nearly Kahler manifolds

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