{"paper":{"title":"A curvature characterization of the Cartan minimal hypersurface in $\\mathbb S^5$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Qing Cui","submitted_at":"2026-07-12T16:42:03Z","abstract_excerpt":"Lawson showed that a non-totally geodesic Einstein minimal hypersurface in $\\mathbb S^5$ is congruent to the Clifford hypersurface $\\mathbb S^2(1/\\sqrt2)\\times \\mathbb S^2(1/\\sqrt2).$ It is also known, by work of Cartan and \\^{O}tsuki, that a non-totally geodesic locally conformally flat minimal hypersurface in $\\mathbb S^5$ is of \\^{O}tsuki type, including the Clifford hypersurface $\\mathbb S^1(1/2)\\times \\mathbb S^3(\\sqrt3/2).$ In this paper we study closed minimal hypersurfaces $M$ in $\\mathbb S^5$ satisfying $|W|^2=2|\\mathring{\\operatorname{Ric}}|^2,$ where $W$ is the Weyl tensor and $\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10827","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/2607.10827/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"}