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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1402.6526","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-02-26T13:04:50Z","cross_cats_sorted":[],"title_canon_sha256":"879c86d1b92afd3b80874a47281a1ea694fc681cf4cb5fc22ffe737ce6ea6b4f","abstract_canon_sha256":"7fffa43933cbb64788c6efa0d65cfe57f6dfc2e3129821040e4cb6447bd184c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:38.553708Z","signature_b64":"UZc1D8zmZa72NU7Rz9PNn7jniorjwRV080+g5G7SHfiAJE/4U2IXqc5Ofh9L4BSKbKE8jjEAEM9IIa/1aCgzBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42c87c0fd249bc3fc6d9b2af3cfd704460b62a8ab31616936834cd52cff78644","last_reissued_at":"2026-05-18T00:57:38.553080Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:38.553080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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