Geodesic orbit metrics on homogeneous spaces constructed by strongly isotropy irreducible spaces

TL;DR

This paper proves that on certain homogeneous spaces built from strongly isotropy irreducible spaces, all geodesic orbit metrics are inherently naturally reductive, advancing understanding of their geometric structure.

Contribution

It establishes that geodesic orbit metrics on these specific homogeneous spaces are necessarily naturally reductive, a new result linking isotropy irreducibility to metric properties.

Findings

All geodesic orbit metrics on these spaces are naturally reductive.

The result applies to spaces constructed from two strongly isotropy irreducible spaces.

This links isotropy irreducibility with the naturally reductive property of metrics.

Abstract

In this paper, we focus on homogeneous spaces which are constructed from two strongly isotropy irreducible spaces, and prove that any geodesic orbit metric on these spaces is naturally reductive.