{"paper":{"title":"Sp(2)/U(1) and a Positive Curvature Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Joseph A. Wolf, Ming Xu","submitted_at":"2015-02-10T02:12:43Z","abstract_excerpt":"A compact Riemannian homogeneous space $G/H$, with a bi--invariant orthogonal decomposition $\\mathfrak{g}=\\mathfrak{h}+\\mathfrak{m}$ is called positively curved for commuting pairs, if the sectional curvature vanishes for any tangent plane in $T_{eH}(G/H)$ spanned by a linearly independent commuting pair in $\\mathfrak{m}$. In this paper,we will prove that on the coset space $\\mathrm{Sp}(2)/\\mathrm{U}(1)$, in which $\\mathrm{U}(1)$ corresponds to a short root, admits positively curved metrics for commuting pairs. B. Wilking recently proved that this $\\mathrm{Sp}(2)/\\mathrm{U}(1)$ can not be posi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02755","kind":"arxiv","version":2},"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"}