{"paper":{"title":"On low-dimensional manifolds with isometric $\\widetilde{\\mathrm{U}}(p,q)$-actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DG","authors_text":"Gestur \\'Olafsson, Raul Quiroga-Barranco","submitted_at":"2015-03-04T22:02:16Z","abstract_excerpt":"Denote by $\\widetilde{\\mathrm{U}}(p,q)$ the universal covering group of $\\mathrm{U}(p,q)$, the linear group of isometries of the pseudo-Hermitian space $\\mathbb{C}^{p,q}$ of signature $p,q$. Let $M$ be a connected analytic complete pseudo-Riemannian manifold that admits an isometric $\\widetilde{\\mathrm{U}}(p,q)$-action and that satisfies $\\dim M \\leq n(n+2)$ where $n = p+q$. We prove that if the action of $\\widetilde{\\mathrm{SU}}(p,q)$ (the connected derived group of $\\widetilde{\\mathrm{U}}(p,q)$) has a dense orbit and the center of $\\widetilde{\\mathrm{U}}(p,q)$ acts non-trivially, then $M$ is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01483","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"}