On the curvature tensor of the Hodge metric of moduli space of polarized Calabi-Yau threefolds

In this article, we give an expression and some estimates of the curvature tensor of the Hodge metric over the moduli space of a polarized calabi-Yau threefold. The symmetricity of the Yukawa coupling is also studied. In the last section of this article, an extra restriction of the limiting Hodge structure for the degeneration of Calabi-Yau threefolds is given.