{"paper":{"title":"Isoparametric hypersurfaces in $\\mathbb{S}^{n}\\times \\mathbb{S}^{m}$ and $\\mathbb{S}^{n}\\times \\mathbb{H}^{m}$","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Huixin Tan, Wenjiao Yan, Yuquan Xie","submitted_at":"2026-02-28T04:02:22Z","abstract_excerpt":"We prove that the angle function associated with the canonical product structure is constant for an isoparametric hypersurface in $\\mathbb{S}^{n}\\times \\mathbb{S}^{m}$, $\\mathbb{S}^{n}\\times \\mathbb{H}^{m}$, or $\\mathbb{H}^{n}\\times \\mathbb{H}^{m}$. This rigidity result enables us to provide a complete classification of isoparametric and homogeneous hypersurfaces in $\\mathbb{S}^{n}\\times \\mathbb{S}^{m}$ and $\\mathbb{S}^{n}\\times \\mathbb{H}^{m}$. Furthermore, we establish a geometric characterization in these two spaces: a hypersurface is isoparametric if and only if it has constant principal c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.00447","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.00447/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}