Integrability of Invariant Geodesic Flows on n-Symmetric Spaces

TL;DR

This paper proves the Liouville integrability of geodesic flows on certain symmetric spaces using a modified argument shift method, extending integrability results to invariant Einstein metrics on n-symmetric spaces.

Contribution

It introduces a modified argument shift method to establish integrability of geodesic flows on n-symmetric spaces with invariant Einstein metrics.

Findings

Liouville integrability of geodesic flows on Ledger-Obata n-symmetric spaces

Extension of integrability results to invariant Einstein metrics

Application of a modified argument shift method

Abstract

In this paper, by modifying the argument shift method,we prove Liouville integrability of geodesic flows of normal metrics (invariant Einstein metrics) on the Ledger-Obata $n$-symmetric spaces $K^n/\diag(K)$, where $K$ is a semisimple (respectively, simple) compact Lie group.