{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6VT6I4557MBK3Y5M5MCLOJR4ZH","short_pith_number":"pith:6VT6I455","schema_version":"1.0","canonical_sha256":"f567e473bdfb02ade3aceb04b7263cc9f3acad082e23c7772040e5573a5c415e","source":{"kind":"arxiv","id":"1704.04702","version":1},"attestation_state":"computed","paper":{"title":"Intrinsic and extrinsic geometry of hypersurfaces in $\\mathbb{S}^n \\times \\mathbb{R}$ and $\\mathbb{H}^n \\times \\mathbb{R}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jo\\~ao Paulo dos Santos, Rafael Novais","submitted_at":"2017-04-16T00:03:19Z","abstract_excerpt":"In this paper, geometric characterizations of conformally flat and radially flat hypersurfaces in $\\mathbb{S}^n \\times \\mathbb{R}$ and $\\mathbb{H}^n \\times \\mathbb{R}$ are given by means of their extrinsic geometry. Under suitable conditions on the shape operator, we classify conformally flat hypersurfaces in terms of rotation hypersurfaces. In addition, a close relation between radially flat hypersurfaces and semi-parallel hypersurfaces is established. These results lead to geometric descriptions of hypersurfaces with special intrinsic structures, such as Einstein metrics, Ricci solitons and "},"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":"1704.04702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-04-16T00:03:19Z","cross_cats_sorted":[],"title_canon_sha256":"882f752f647a410c40f21828681b027bd73bad236b4b9a7bb9629b78ea5379b1","abstract_canon_sha256":"6156fe69c57fa3547915c43e4174f2dab8820ffe80adf29ce4c436b7cde9b714"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:17.909795Z","signature_b64":"0/4wKgRio/7kf8RZtllxTHEHID1OFFdpCZMjs54dUUWQnhB3VoAbVn+l4weZzV9QDwSPeDgklDs5t/ERvCczDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f567e473bdfb02ade3aceb04b7263cc9f3acad082e23c7772040e5573a5c415e","last_reissued_at":"2026-05-18T00:46:17.909453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:17.909453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intrinsic and extrinsic geometry of hypersurfaces in $\\mathbb{S}^n \\times \\mathbb{R}$ and $\\mathbb{H}^n \\times \\mathbb{R}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jo\\~ao Paulo dos Santos, Rafael Novais","submitted_at":"2017-04-16T00:03:19Z","abstract_excerpt":"In this paper, geometric characterizations of conformally flat and radially flat hypersurfaces in $\\mathbb{S}^n \\times \\mathbb{R}$ and $\\mathbb{H}^n \\times \\mathbb{R}$ are given by means of their extrinsic geometry. Under suitable conditions on the shape operator, we classify conformally flat hypersurfaces in terms of rotation hypersurfaces. In addition, a close relation between radially flat hypersurfaces and semi-parallel hypersurfaces is established. These results lead to geometric descriptions of hypersurfaces with special intrinsic structures, such as Einstein metrics, Ricci solitons and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04702","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":""},"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":"1704.04702","created_at":"2026-05-18T00:46:17.909508+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.04702v1","created_at":"2026-05-18T00:46:17.909508+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.04702","created_at":"2026-05-18T00:46:17.909508+00:00"},{"alias_kind":"pith_short_12","alias_value":"6VT6I4557MBK","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6VT6I4557MBK3Y5M","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6VT6I455","created_at":"2026-05-18T12:31:03.183658+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/6VT6I4557MBK3Y5M5MCLOJR4ZH","json":"https://pith.science/pith/6VT6I4557MBK3Y5M5MCLOJR4ZH.json","graph_json":"https://pith.science/api/pith-number/6VT6I4557MBK3Y5M5MCLOJR4ZH/graph.json","events_json":"https://pith.science/api/pith-number/6VT6I4557MBK3Y5M5MCLOJR4ZH/events.json","paper":"https://pith.science/paper/6VT6I455"},"agent_actions":{"view_html":"https://pith.science/pith/6VT6I4557MBK3Y5M5MCLOJR4ZH","download_json":"https://pith.science/pith/6VT6I4557MBK3Y5M5MCLOJR4ZH.json","view_paper":"https://pith.science/paper/6VT6I455","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.04702&json=true","fetch_graph":"https://pith.science/api/pith-number/6VT6I4557MBK3Y5M5MCLOJR4ZH/graph.json","fetch_events":"https://pith.science/api/pith-number/6VT6I4557MBK3Y5M5MCLOJR4ZH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6VT6I4557MBK3Y5M5MCLOJR4ZH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6VT6I4557MBK3Y5M5MCLOJR4ZH/action/storage_attestation","attest_author":"https://pith.science/pith/6VT6I4557MBK3Y5M5MCLOJR4ZH/action/author_attestation","sign_citation":"https://pith.science/pith/6VT6I4557MBK3Y5M5MCLOJR4ZH/action/citation_signature","submit_replication":"https://pith.science/pith/6VT6I4557MBK3Y5M5MCLOJR4ZH/action/replication_record"}},"created_at":"2026-05-18T00:46:17.909508+00:00","updated_at":"2026-05-18T00:46:17.909508+00:00"}