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arXiv · 1202.0183

Hessian of the natural Hermitian form on twistor spaces

Guillaume Deschamps·Noël Le Du·Christophe Mourougane
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Abstract

We compute the hessian of the natural Hermitian form successively on the Calabi family of a hyperkähler manifold, on the twistor space of a 4-dimensional anti-self-dual Riemannian manifold and on the twistor space of a quaternionic Kähler manifold. We show a strong convexity property of the cycle space of twistor lines on the Calabi family of a hyperkähler manifold. We also prove convexity properties of the 1-cycle space of the twistor space of a 4-dimensional anti-self-dual Einstein manifold of non-positive scalar curvature and of the 1-cycle space of the twistor space of a quaternionic Kähler manifold of non-positive scalar curvature. We check that no non-Kähler strong KT manifold occurs as such a twistor space.

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Guillaume Deschamps, Noël Le Du, Christophe Mourougane. 2013-10-24. Hessian of the natural Hermitian form on twistor spaces. https://doi.org/10.24033/bsmf.2729

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