{"paper":{"title":"Pseudo-Riemannian $\\mathrm{G}_{2(2)}$-manifolds with dimension at most $21$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"R. Quiroga-Barranco","submitted_at":"2015-10-22T22:41:21Z","abstract_excerpt":"Let $G_{2(2)}$ be the non-compact connected simple Lie group of type $G_2$ over $\\mathbb{R}$, and let $M$ be a connected analytic complete pseudo-Riemannian manifold that admits an isometric $G_{2(2)}$-action with a dense orbit. For the case $\\dim(M) \\leq 21$, we provide a full description of the manifold $M$, its geometry and its $G_{2(2)}$-action. The latter are always given in terms of a Lie group geometry related to $G_{2(2)}$, and in one case $M$ is essentially the quotient of $\\widetilde{\\mathrm{S0}}_0(3,4)$ by a lattice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06782","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"}