Four-dimensional naturally reductive pseudo-Riemannian spaces

TL;DR

This paper classifies 4-dimensional naturally reductive pseudo-Riemannian spaces, including symmetric spaces, product spaces, and new indecomposable manifolds, with analysis of the oscillator group within this framework.

Contribution

It provides the first comprehensive classification of 4D naturally reductive pseudo-Riemannian spaces, introducing new indecomposable examples and analyzing the oscillator group.

Findings

Classification includes symmetric and product spaces

Introduction of new indecomposable manifolds

Analysis of the oscillator group within the classification

Abstract

The classification of 4-dimensional naturally reductive pseudo-Riemannian spaces is given. This classification comprises symmetric spaces, the product of 3-dimensional naturally reductive spaces with the real line and new families of indecomposable manifolds which are studied at the end of the article. The oscillator group is also analyzed from the point of view of this classification.