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 the Kodaira dimension of X is zero. We provide examples in the case M=GxG, where G is a compact connected real Lie group. Finally we describe geometrical properties of real parallelizable manifolds in the framework of statistical geometry.