The classification of 7- and 8-dimensional naturally reductive spaces

TL;DR

This paper introduces a new classification method for naturally reductive spaces, successfully categorizing all such spaces in dimensions 7 and 8 using advanced structure theory and novel constructions.

Contribution

It presents a new classification approach based on recent structure theory, leading to a complete classification of 7- and 8-dimensional naturally reductive spaces.

Findings

Complete classification of 7-dimensional naturally reductive spaces

Complete classification of 8-dimensional naturally reductive spaces

New construction techniques for naturally reductive spaces

Abstract

A new method for classifying naturally reductive spaces is presented. This method relies on the structure theory of naturally reductive spaces developed in \cite{Storm2018a} and the new construction of naturally reductive spaces in \cite{Storm2018}. We obtain the classification of all naturally reductive spaces in dimension 7 and 8.