{"paper":{"title":"Closed Minimal Hypersurfaces in $\\mathbb{S}^5(1)$ with Constant Scalar and Gauss-Kronecker Curvatures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Qintao Deng, Yunjia Kou","submitted_at":"2026-07-05T18:50:19Z","abstract_excerpt":"In this paper, we prove that any closed minimal hypersurface $M^4$ of $\\mathbb{S}^5(1)$ with constant scalar curvature and constant Gauss-Kronecker curvature must be isoparametric. Specifically, $M^4$ is either an equatorial 4-sphere, a Clifford torus $\\mathbb{S}^2\\left(\\frac{\\sqrt{2}}{2}\\right)\\times \\mathbb{S}^2\\left(\\frac{\\sqrt{2}}{2}\\right)$ or $\\mathbb{S}^1\\left(\\frac{1}{2}\\right)\\times \\mathbb{S}^3\\left(\\frac{\\sqrt{3}}{2}\\right)$, or a Cartan's minimal hypersurface. Consequently, the squared norm of the second fundamental form $S$ can only take the values 0, 4, 12. This result provides s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06588","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.06588/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"}