Completeness of projective special Kähler and quaternionic Kähler manifolds

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

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