Homogeneous pseudo-Riemannian structures of metrics of Kaluza-Klein type on the three-dimensional anti-de Sitter spacetime

TL;DR

This paper classifies homogeneous pseudo-Riemannian and almost contact structures of Kaluza-Klein type on 3D anti-de Sitter spacetime, detailing their isometry groups and reductive decompositions.

Contribution

It provides a comprehensive classification of these geometric structures and their symmetry groups on the three-dimensional anti-de Sitter spacetime.

Findings

Classification of homogeneous pseudo-Riemannian structures

Classification of homogeneous almost contact and paracontact structures

Identification of isometry groups and reductive decompositions

Abstract

We classify homogeneous pseudo-Riemannian structures of a three-parameter family of metrics called Kaluza-Klein type on the three-dimensional anti-de Sitter spacetime with their induced groups of isometries and reductive decompositions. We also obtain the classification of homogeneous almost contact and paracontact metric structures of metrics of Kaluza-Klein type on the three-dimensional anti-de Sitter spacetime with their isometry groups and reductive decompositions.