{"paper":{"title":"On low-dimensional manifolds with isometric $\\mathrm{SO}_0(p,q)$-actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gestur Olafsson, Raul Quiroga-Barranco","submitted_at":"2010-03-02T23:04:26Z","abstract_excerpt":"Let $G$ be a non-compact simple Lie group with Lie algebra $\\mathfrak{g}$. Denote with $m(\\mathfrak{g})$ the dimension of the smallest non-trivial $\\mathfrak{g}$-module with an invariant non-degenerate symmetric bilinear form. For an irreducible finite volume pseudo-Riemannian analytic manifold $M$ it is observed that $\\dim(M) \\geq \\dim(G) + m(\\mathfrak{g})$ when $M$ admits an isometric $G$-action with a dense orbit. The Main Theorem considers the case $G = \\widetilde{\\mathrm{SO}}_0(p,q)$ providing an explicit description of $M$ when the bound is achieved. In such case, $M$ is (up to a finite "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0704","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"}