Lie groups of dimension 4 and almost hypercomplex manifolds with Hermitian-Norden metrics

TL;DR

This paper explores 4-dimensional Lie groups to classify and analyze almost hypercomplex manifolds with Hermitian-Norden metrics, revealing relationships between Lie algebra classifications and geometric properties.

Contribution

It establishes a connection between Lie algebra classifications and the geometric classification of almost hypercomplex manifolds with Hermitian-Norden metrics.

Findings

Classified 4-dimensional indecomposable real Lie algebras

Analyzed geometric characteristics of the manifolds

Linked algebraic classifications to geometric properties

Abstract

Object of investigation are almost hypercomplex manifolds with Hermitian-Norden metrics of the lowest dimension. The considered manifolds are constructed on 4-dimensional Lie groups. It is established a relation between the classes of a classification of 4-dimensional indecomposable real Lie algebras and the classification of the manifolds under study. The basic geometrical characteristics of the constructed manifolds are studied in the frame of the mentioned classification of the Lie algebras.