Some results of quantum correction on compact Calabi-Yau manifolds of dimension 3 and 4

It is shown that for compact Calabi-Yau threefolds, “no strong quantum correction” is equivalent to the condition that, with respect to the Hodge metric, the image Φ(T) of the Teichmüller space T under the period map Φ is an open submanifold W of the same dimension as T. In this paper, we extend this result to the case of dimension 4. We also obtained similar results for compact generalized Calabi-Yau manifolds in dimension 3 and 4, under the assumption that their Teichmüller space T exists and is a simply connected complex manifold.