{"paper":{"title":"Hypersurfaces with Constant Ricci Eigenvalues in Real Space Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jianquan Ge, Yuyang Zhao","submitted_at":"2026-06-11T15:12:59Z","abstract_excerpt":"The classification of curvature homogeneous hypersurfaces in real space forms was established by Tsukada in 1988, with the remaining rank-two cases in $\\mathbb{S}^4$ and $\\mathbb{H}^4$ settled by Bryant-Florit-Ziller in 2025. It is obvious that curvature homogeneity implies constant Ricci eigenvalues. In this paper, we prove that for hypersurfaces in real space forms, the converse also holds: a connected hypersurface immersed in real space forms has constant Ricci eigenvalues if and only if it is curvature homogeneous. Hence, hypersurfaces with constant Ricci eigenvalues in real space forms ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13455","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/2606.13455/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"}