{"paper":{"title":"Hypersurfaces of $\\mathbb{H}^2\\times\\mathbb{H}^2$ with constant sectional curvature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Haizhong Li, Luc Vrancken, Xianfeng Wang, Zeke Yao","submitted_at":"2026-06-23T15:16:03Z","abstract_excerpt":"In this paper, we classify the hypersurfaces of $\\mathbb{H}^2\\times\\mathbb{H}^2$ with constant sectional curvature. In contrast to $\\mathbb{S}^2\\times\\mathbb{S}^2$, the resulting examples for $\\mathbb{H}^2\\times\\mathbb{H}^2$ exhibit more diversity, and we construct a special example with non-constant product angle function. For $\\mathbb{S}^2\\times\\mathbb{S}^2$, however, the product angle function of any constant sectional curvature hypersurface is identically zero. As a byproduct, we classify the hypersurfaces of $\\mathbb{H}^2\\times\\mathbb{H}^2$ with constant product angle function and constan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24686","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/2606.24686/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"}