Almost complex parallelizable manifolds: Kodaira dimension and special structures

TL;DR

This paper investigates the Kodaira dimension of almost complex parallelizable manifolds, providing conditions for when it equals zero, with examples involving Lie groups, and explores their geometric properties in statistical geometry.

Contribution

It establishes criteria for the Kodaira dimension of such manifolds, offers explicit examples with Lie groups, and connects their geometry to statistical geometry frameworks.

Findings

Conditions for Kodaira dimension zero in almost complex parallelizable manifolds

Explicit examples involving products of compact Lie groups

Description of geometric properties within statistical geometry

Abstract

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 $\operatorname{kod}(X) = 0$. 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.