Almost complex parallelizable manifolds: Kodaira dimension and special structures

We study the Kodaira dimension of a real parallelizable manifold $M$, with an almost complex structure $J$ in standard form with respect to a given parallelism. For $X=(M,J)$ we give conditions under which $\mathrm{kod}(X)=0$. We provide examples in the case $M=G\times G$, where $G$ is a compact connected real Lie group. Finally we describe geometrical properties of real parallelizable manifolds in the framework of statistical geometry.