A new construction of naturally reductive spaces

TL;DR

This paper introduces a novel method for constructing naturally reductive spaces, significantly expanding the known families, with explicit models and isometry groups provided for these new geometries.

Contribution

It presents a new construction technique for naturally reductive spaces, including explicit models and isometry groups, broadening the scope of known examples.

Findings

Constructed a large new class of naturally reductive spaces.

Provided explicit infinitesimal models and isometry groups.

Demonstrated the natural reductive structure explicitly.

Abstract

A new construction of naturally reductive spaces is presented. This construction gives a large amount of new families of naturally reductive spaces. First the infinitesimal models of the new naturally reductive spaces are constructed. A concrete transitive group of isometries is given for the new spaces and also the naturally reductive structure with respect to this group is explicitly given.