Deformations of Manifolds of Calabi-Yau Type

In 2011, A. Iliev and L. Manivel proposed the class of manifolds of Calabi-Yau type as a generalization of Calabi-Yau threefolds that would include K{\"a}hler mirror pairs even for threefolds with $h^{2,1}=0$. We construct sufficient conditions for such manifolds to have unobstructed deformations even in the non-Fano case. In such cases where the deformations are unobstructed, we consider two metrics on the moduli space of such manifolds, one equivalent to the Weil-Petersson metric and the other the resulting partial Hodge metrics. Curvature tensors for both metrics are produced, and bounds are found for holomorphic bisectional curvature and holomorphic sectional curvature for a specific partial Hodge metric on the moduli space. Finally, a formula is found relating these metrics, the Euler characteristic, and the BCOV torsion on manifolds of Calabi-Yau type