{"paper":{"title":"Canonical sphere bundles of the Grassmann manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"math.DG","authors_text":"Eduardo Chiumiento, Esteban Andruchow, Gabriel Larotonda","submitted_at":"2018-03-02T22:06:53Z","abstract_excerpt":"For a given Hilbert space $\\mathcal H$, consider the space of self-adjoint projections $\\mathcal P(\\mathcal H)$. In this paper we study the differentiable structure of a canonical sphere bundle over $\\mathcal P(\\mathcal H)$ given by $$ \\mathcal R=\\{\\, (P,f)\\in \\mathcal P(\\mathcal H)\\times \\mathcal H \\, : \\, Pf=f , \\, \\|f\\|=1\\, \\}. $$ We establish the smooth action on $\\mathcal R$ of the group of unitary operators of $\\mathcal H$, therefore $\\mathcal R$ is an homogeneous space. Then we study the metric structure of $\\mathcal R$ by endowing it first with the uniform quotient metric, which is a F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01057","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"}