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)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X = (M, J)$$\end{document} we give conditions under which kod(X)=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\textrm{kod}\,}}(X) = 0$$\end{document}. We provide examples in the case M=G×G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M = G \times G$$\end{document}, where G is a compact connected real Lie group. Finally we describe geometrical properties of real parallelizable manifolds in the framework of statistical geometry.