J. reine angew. Math. 588 (2005), 49—69


We establish an unexpected relation among the Weil-Petersson metric, the generalized Hodge metrics and the BCOV torsion. Using this relation, we prove that certain kind of moduli spaces of polarized Calabi-Yau manifolds do not admit complete subvarieties. That is, there is no complete smooth family for certain class of polarized Calabi-Yau manifolds. We… (More)