{"paper":{"title":"Rigid geometric structures, isometric actions, and algebraic quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jinpeng An","submitted_at":"2010-05-09T19:53:31Z","abstract_excerpt":"By using a Borel density theorem for algebraic quotients, we prove a theorem concerning isometric actions of a Lie group $G$ on a smooth or analytic manifold $M$ with a rigid $\\mathrm{A}$-structure $\\sigma$. It generalizes Gromov's centralizer and representation theorems to the case where $R(G)$ is split solvable and $G/R(G)$ has no compact factors, strengthens a special case of Gromov's open dense orbit theorem, and implies that for smooth $M$ and simple $G$, if Gromov's representation theorem does not hold, then the local Killing fields on $\\widetilde{M}$ are highly non-extendable. As applic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1423","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"}