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We investigate hypersurfaces M in space forms N satisfying (A). The main result states that if the tensor C.R - R.C of a non-quasi-Einstein hypersurface M in N is a linear combination of the tensors Q(g,C) and Q(S,C) then (A) holds on M. In the case when M is a quasi-Einstein hypersurface in N and some additional assumptions are satisfied then (A) also holds on M."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.01402","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-02T17:53:01Z","cross_cats_sorted":[],"title_canon_sha256":"460773b9d23909f75fbaad7aff9e56edb007095e0565f7752d52c0f57a008ecd","abstract_canon_sha256":"90541d9433a70bf523caf068f7dc5e300f4894f905767c1fbf195ace5967d6a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:05.006616Z","signature_b64":"utTL1dsafi7eS98Pqi9MvLS5b8EuwqFhwP3h6jCNQ3f6ais2SFbF7y/WIewN4+aXwgFeFFR0QSjJy+O1yiYaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1019fc256cb0fda918228475304d32d50635fd24f10832d062311b4db3c54fc","last_reissued_at":"2026-05-17T23:52:05.006224Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:05.006224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hypersurfaces in space forms satisfying some generalized Einstein metric condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Georges Zafindratafa, Malgorzata Glogowska, Ryszard Deszcz","submitted_at":"2018-10-02T17:53:01Z","abstract_excerpt":"The difference tensor C.R - R.C of Einstein manifolds, some quasi-Einstein manifolds and Roter type manifolds, of dimension n > 3, satisfy the following curvature condition: (A) C.R - R.C = Q(S,C) - (k /(n-1)) Q(g,C). We investigate hypersurfaces M in space forms N satisfying (A). The main result states that if the tensor C.R - R.C of a non-quasi-Einstein hypersurface M in N is a linear combination of the tensors Q(g,C) and Q(S,C) then (A) holds on M. 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