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 kod (X) = 0 . We provide examples in the case M = G × 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.