Completeness of projective special Kähler and quaternionic Kähler manifolds

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We prove that every projective special Kähler manifold with regular boundary behaviour is complete and defines a family of complete quaternionic Kähler manifolds depending on a parameter c≥ 0. We also show that, irrespective of its boundary behaviour, every complete projective special Kähler manifold with cubic prepotential gives rise to such a family. Examples include non-trivial deformations of non-compact symmetric quaternionic Kähler manifolds.