Geodesic flows on Riemannian g.o. spaces

TL;DR

This paper proves that geodesic flows on certain Riemannian homogeneous spaces, including g.o. spaces of compact Lie groups, are integrable, expanding understanding of their geometric and dynamical properties.

Contribution

It establishes the integrability of geodesic flows on Riemannian g.o. spaces of compact Lie groups and related homogeneous spaces with principal bundle structures.

Findings

Geodesic flows on g.o. spaces are integrable.

Integrability extends to related homogeneous spaces with principal bundle structures.

Enhances understanding of dynamical systems on Riemannian homogeneous spaces.

Abstract

We prove the integrability of geodesic flows on the Riemannian g.o. spaces of compact Lie groups, as well as on a related class of Riemannian homogeneous spaces having an additional principal bundle structure.