{"paper":{"title":"Isoparametric hypersurfaces with four principal curvatures, III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Quo-Shin Chi","submitted_at":"2011-04-16T17:38:01Z","abstract_excerpt":"The classification work [5], [9] left unsettled only those anomalous isoparametric hypersurfaces with four principal curvatures and multiplicity pair $\\{4,5\\},\\{6,9\\}$ or $\\{7,8\\}$ in the sphere.\n  By systematically exploring the ideal theory in commutative algebra in conjunction with the geometry of isoparametric hypersurfaces, we show that an isoparametric hypersurface with four principal curvatures and multiplicities $\\{4,5\\}$ in $S^{19}$ is homogeneous, and, moreover, an isoparametric hypersurface with four principal curvatures and multiplicities $\\{6,9\\}$ in $S^{31}$ is either the inhomog"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3249","kind":"arxiv","version":3},"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"}