Key points are not available for this paper at this time.
The classical Weil-Petersson metric on the Teichmüller space of compact Riemann surfaces is a Kähler metric, which is complete only in the case of elliptic curves Wo. It has a natural generalization to the deformation spaces of higher dimansional polarized Kähler-Einstein
Chin-Lung Wang (Wed,) studied this question.