{"paper":{"title":"Integrability of geodesic flows for metrics on suborbits of the adjoint orbits of compact groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ihor V. Mykytyuk","submitted_at":"2014-02-26T13:04:50Z","abstract_excerpt":"Let $G/K$ be an orbit of the adjoint representation of a compact connected Lie group $G$, $\\sigma$ be an involutive automorphism of $G$ and $\\tilde G$ be the Lie group of fixed points of $\\sigma$. We find a sufficient condition for the complete integrability of the geodesic flow of the Riemannian metric on $\\tilde G/(\\tilde G\\cap K)$, which is induced by the bi-invariant Riemannian metric on $\\tilde G$. The integrals constructed here are real analytic functions, polynomial in momenta. It is checked that this sufficient condition holds when $G$ is the unitary group $U(n)$ and $\\sigma$ is its au"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6526","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}