{"paper":{"title":"Riemannian symmetries in flag manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Elisabeth Remm, Paola Piu","submitted_at":"2012-04-11T13:26:08Z","abstract_excerpt":"Flag manifolds are in general not symmetric spaces. But they are provided with a structure of $\\mathbb{Z}_2^k$-symmetric space. We describe the Riemannian metrics adapted to this structure and some properties of reducibility. We detail for the flag manifold $SO(5)/SO(2)\\times SO(2) \\times SO(1)$ what are the conditions for a metric adapted to the $\\mathbb{Z}_2^2$-symmetric structure to be naturally reductive."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2440","kind":"arxiv","version":1},"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"}