{"paper":{"title":"Spherical gradient manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Christian Miebach, Henrik Stoetzel","submitted_at":"2009-08-27T12:27:52Z","abstract_excerpt":"We study the action of a real-reductive group $G=K\\exp(\\lie{p})$ on real-analytic submanifold $X$ of a K\\\"ahler manifold $Z$. We suppose that the action of $G$ extends holomorphically to an action of the complexified group $G^\\mbb{C}$ such that the action of a maximal Hamiltonian subgroup is Hamiltonian. The moment map $\\mu$ induces a gradient map $\\mu_\\lie{p}\\colon X\\to\\lie{p}$. We show that $\\mu_\\lie{p}$ almost separates the $K$--orbits if and only if a minimal parabolic subgroup of $G$ has an open orbit. This generalizes Brion's characterization of spherical K\\\"ahler manifolds with moment m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.3998","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"}