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We then apply the equation to show that the generalized\n  Chen's conjecture is true for totally umbilical biharmonic hypersurfaces in an Einstein space, and construct a (2-parameter) family of conformally flat metrics and a (4-parameter) family of multiply warped product metrics each of which turns the foliation of an upper-half space of $\\math"},"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":"0901.1507","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-01-12T16:54:40Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"da5404549ba5ba16e922b12a46f1ffb9c2b43075fe38360b99ad85705540adf4","abstract_canon_sha256":"2762eeeb7c81216bb31551abb9e267653d9aa4d748e4033b7b5cf9b406538ee1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:20.036284Z","signature_b64":"55yHuU+DjVQvzzB9+dDwiQtajk/kWxA3q1jbbi8QLbj1SXnw2WatiFivOFgPYnWKH2uQ4eLmdh1DPhv5DwCqCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d47c7f2da0387bb35b5050fa3f55232e2acddcce7f46341811f592887694705","last_reissued_at":"2026-05-18T04:32:20.035630Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:20.035630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Biharmonic hypersurfaces in Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Ye-Lin Ou","submitted_at":"2009-01-12T16:54:40Z","abstract_excerpt":"We study biharmonic hypersurfaces in a generic Riemannian manifold. 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