Structure theory of naturally reductive spaces

TL;DR

This paper provides a comprehensive construction formula for all naturally reductive spaces, enabling explicit analysis of their reducibility and isomorphism properties.

Contribution

It introduces a general explicit construction for naturally reductive spaces and establishes criteria for their reducibility and isomorphism.

Findings

Derived a general formula for naturally reductive spaces

Proved criteria for reducibility of these spaces

Established isomorphism conditions among them

Abstract

The main result of this paper is that every naturally reductive space can be explicitly constructed from the construction in \cite{Storm2018}. This gives us a general formula for any naturally reductive space and from this we prove reducibility and isomorphism criteria.