Almost hypercomplex manifolds with Hermitian-Norden metrics and 4-dimensional indecomposable real Lie algebras depending on two parameters

TL;DR

This paper classifies 4-dimensional indecomposable real Lie algebras depending on two parameters and explores the geometric properties of the associated almost hypercomplex manifolds with Hermitian-Norden metrics.

Contribution

It provides a classification of certain Lie algebras and analyzes the geometric structures of the corresponding manifolds with Hermitian-Norden metrics.

Findings

Classification of 4-dimensional indecomposable real Lie algebras depending on two parameters.

Identification of geometric characteristics of almost hypercomplex manifolds with Hermitian-Norden metrics.

Insights into the structure of manifolds arising from these Lie algebras.

Abstract

The object of investigations are almost hypercomplex structures with Hermitian-Norden metrics on 4-dimensional Lie groups considered as smooth manifolds. There are studied both the basic classes of a classification of 4-dimensional indecomposable real Lie algebras depending on two parameters. Some geometric characteristics of the respective almost hypercomplex manifolds with Hermitian-Norden metrics are obtained.