A survey on locally Homogeneous almost-Hermitian spaces

TL;DR

This survey reviews the theory of locally homogeneous almost-Hermitian spaces, focusing on curvature formulas for Gauduchon connections and providing explicit computational examples.

Contribution

It introduces a framework using varying Lie brackets to derive curvature formulas and offers explicit examples, advancing understanding of these geometric structures.

Findings

Formulas for curvature of Gauduchon connections

Explicit computational examples provided

Framework using varying Lie brackets introduced

Abstract

We survey the theory of locally homogeneous almost-Hermitian spaces. In particular, by using the framework of varying Lie brackets, we write formulas for the curvature of all the Gauduchon connections and we provide explicit examples of computations.