Naturally reductive pseudo-Riemannian spaces

TL;DR

This paper constructs a new family of naturally reductive pseudo-Riemannian spaces using Lie algebra representations with ad-invariant metrics, exploring their geometry and homogeneous structures.

Contribution

It introduces novel examples of naturally reductive pseudo-Riemannian spaces derived from Lie algebra representations, expanding the understanding of their geometric properties.

Findings

Exhibition of peculiar examples of such spaces

Detailed study of their geometric structure

Characterization of their naturally reductive homogeneous structure

Abstract

A family of naturally reductive pseudo-Riemannian spaces is constructed out of the representations of Lie algebras with ad-invariant metrics. We exhibit peculiar examples, study their geometry and characterize the corresponding naturally reductive homogeneous structure.