{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:LYQNHZ63U5R3VN64ALIAJG4BBD","short_pith_number":"pith:LYQNHZ63","schema_version":"1.0","canonical_sha256":"5e20d3e7dba763bab7dc02d0049b8108e342c41364335de5c68a7d7730f0fcce","source":{"kind":"arxiv","id":"1306.6069","version":4},"attestation_state":"computed","paper":{"title":"On biharmonic submanifolds in non-positively curved manifolds","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Yong Luo","submitted_at":"2013-06-25T19:42:04Z","abstract_excerpt":"In the biharmonic submanifolds theory there is a generalized Chen's conjecture which states that biharmonic submanifolds in a Riemannian manifold with non-positive sectional curvature must be minimal. This conjecture turned out false by a counter example of Y. L. Ou and L. Tang in \\cite{Ou-Ta}. However it remains interesting to find out sufficient conditions which guarantee this conjecture to be true. In this note we prove that:\n  1. Any complete biharmonic submanifold (resp. hypersurface) $(M, g)$ in a Riemannian manifold $(N, h)$ with non-positive sectional curvature (resp. Ricci curvature) "},"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":"1306.6069","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2013-06-25T19:42:04Z","cross_cats_sorted":[],"title_canon_sha256":"597cbf84f5f84f38f9b90d342f69be60b04bac6593de8b6be972d02a7b34eeba","abstract_canon_sha256":"4f884f045ef36b240105a5d9bed73b94e8d934b669a7020fe49d6d1657bdc175"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:51.840125Z","signature_b64":"O2apBGbPS3aclAsrLwYAGDdMiMir9pKdlHuvx3/wSanRVA4QJTTpdfRb0BEleYEMAUk7kmKEiUEzftvpFL9DDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e20d3e7dba763bab7dc02d0049b8108e342c41364335de5c68a7d7730f0fcce","last_reissued_at":"2026-05-18T02:50:51.839557Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:51.839557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On biharmonic submanifolds in non-positively curved manifolds","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Yong Luo","submitted_at":"2013-06-25T19:42:04Z","abstract_excerpt":"In the biharmonic submanifolds theory there is a generalized Chen's conjecture which states that biharmonic submanifolds in a Riemannian manifold with non-positive sectional curvature must be minimal. This conjecture turned out false by a counter example of Y. L. Ou and L. Tang in \\cite{Ou-Ta}. However it remains interesting to find out sufficient conditions which guarantee this conjecture to be true. In this note we prove that:\n  1. Any complete biharmonic submanifold (resp. hypersurface) $(M, g)$ in a Riemannian manifold $(N, h)$ with non-positive sectional curvature (resp. Ricci curvature) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6069","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1306.6069","created_at":"2026-05-18T02:50:51.839649+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.6069v4","created_at":"2026-05-18T02:50:51.839649+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.6069","created_at":"2026-05-18T02:50:51.839649+00:00"},{"alias_kind":"pith_short_12","alias_value":"LYQNHZ63U5R3","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LYQNHZ63U5R3VN64","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LYQNHZ63","created_at":"2026-05-18T12:27:51.066281+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LYQNHZ63U5R3VN64ALIAJG4BBD","json":"https://pith.science/pith/LYQNHZ63U5R3VN64ALIAJG4BBD.json","graph_json":"https://pith.science/api/pith-number/LYQNHZ63U5R3VN64ALIAJG4BBD/graph.json","events_json":"https://pith.science/api/pith-number/LYQNHZ63U5R3VN64ALIAJG4BBD/events.json","paper":"https://pith.science/paper/LYQNHZ63"},"agent_actions":{"view_html":"https://pith.science/pith/LYQNHZ63U5R3VN64ALIAJG4BBD","download_json":"https://pith.science/pith/LYQNHZ63U5R3VN64ALIAJG4BBD.json","view_paper":"https://pith.science/paper/LYQNHZ63","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.6069&json=true","fetch_graph":"https://pith.science/api/pith-number/LYQNHZ63U5R3VN64ALIAJG4BBD/graph.json","fetch_events":"https://pith.science/api/pith-number/LYQNHZ63U5R3VN64ALIAJG4BBD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LYQNHZ63U5R3VN64ALIAJG4BBD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LYQNHZ63U5R3VN64ALIAJG4BBD/action/storage_attestation","attest_author":"https://pith.science/pith/LYQNHZ63U5R3VN64ALIAJG4BBD/action/author_attestation","sign_citation":"https://pith.science/pith/LYQNHZ63U5R3VN64ALIAJG4BBD/action/citation_signature","submit_replication":"https://pith.science/pith/LYQNHZ63U5R3VN64ALIAJG4BBD/action/replication_record"}},"created_at":"2026-05-18T02:50:51.839649+00:00","updated_at":"2026-05-18T02:50:51.839649+00:00"}