{"paper":{"title":"On the topology and the geometry of SO(3)-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AT","math.MP"],"primary_cat":"math.DG","authors_text":"Ilka Agricola, Julia Becker-Bender, Thomas Friedrich","submitted_at":"2010-10-01T20:28:21Z","abstract_excerpt":"Consider the nonstandard embedding of SO(3) into SO(5) given by the 5-dimensional irreducible representation of SO(3), henceforth called SO(3)_\\ir. In this note, we study the topology and the differential geometry of 5-dimensional Riemannian manifolds carrying such an SO(3)_\\ir structure, i.\\,e. with a reduction of the frame bundle to SO(3)_\\ir."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0260","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"}