{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:Y6N5NIFGXMTWUZA6ESKVKVZCLV","short_pith_number":"pith:Y6N5NIFG","schema_version":"1.0","canonical_sha256":"c79bd6a0a6bb276a641e24955557225d6352c645919a55ae7823d0b412f88088","source":{"kind":"arxiv","id":"1105.0813","version":2},"attestation_state":"computed","paper":{"title":"Constant Angle Surfaces in Product Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Daniel Kowalczyk, Franki Dillen","submitted_at":"2011-05-04T12:59:53Z","abstract_excerpt":"We classify all the surfaces in $M^2(c_1)\\times M^2(c_2)$ for which the tangent space $T_pM^2$ makes constant angles with $T_p(M^2(c_1)\\times \\{p_2\\})$ (or equivalently with $T_p(\\{p_1\\}\\times M^2(c_2))$ for every point $p=(p_1,p_2)$ of $M^2$. Here $M^2(c_1)$ and $M^2(c_2)$ are 2-dimensional space forms, not both flat. As a corollary we give a classification of all the totally geodesic surfaces in $M^2(c_1)\\times M^2(c_2)$."},"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":"1105.0813","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-04T12:59:53Z","cross_cats_sorted":[],"title_canon_sha256":"316d522836c3532b1ba57dd759c56d248caf9653cc36498436a94ef394b7bcd8","abstract_canon_sha256":"542c14a817b482e7b6bf0b344401d25386006decd750e4882eceefcf7934574a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:02:08.962043Z","signature_b64":"zbIprDlVX9lceUI/VJnxyGo+Wifxh7T3YU5sL9/MBckCZ+qzXJMDN23azwyYXdTGtH/hvaI+Vke6ctRXP14gAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c79bd6a0a6bb276a641e24955557225d6352c645919a55ae7823d0b412f88088","last_reissued_at":"2026-05-18T02:02:08.961429Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:02:08.961429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constant Angle Surfaces in Product Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Daniel Kowalczyk, Franki Dillen","submitted_at":"2011-05-04T12:59:53Z","abstract_excerpt":"We classify all the surfaces in $M^2(c_1)\\times M^2(c_2)$ for which the tangent space $T_pM^2$ makes constant angles with $T_p(M^2(c_1)\\times \\{p_2\\})$ (or equivalently with $T_p(\\{p_1\\}\\times M^2(c_2))$ for every point $p=(p_1,p_2)$ of $M^2$. Here $M^2(c_1)$ and $M^2(c_2)$ are 2-dimensional space forms, not both flat. As a corollary we give a classification of all the totally geodesic surfaces in $M^2(c_1)\\times M^2(c_2)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0813","kind":"arxiv","version":2},"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":"1105.0813","created_at":"2026-05-18T02:02:08.961517+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.0813v2","created_at":"2026-05-18T02:02:08.961517+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0813","created_at":"2026-05-18T02:02:08.961517+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y6N5NIFGXMTW","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y6N5NIFGXMTWUZA6","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y6N5NIFG","created_at":"2026-05-18T12:26:47.523578+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/Y6N5NIFGXMTWUZA6ESKVKVZCLV","json":"https://pith.science/pith/Y6N5NIFGXMTWUZA6ESKVKVZCLV.json","graph_json":"https://pith.science/api/pith-number/Y6N5NIFGXMTWUZA6ESKVKVZCLV/graph.json","events_json":"https://pith.science/api/pith-number/Y6N5NIFGXMTWUZA6ESKVKVZCLV/events.json","paper":"https://pith.science/paper/Y6N5NIFG"},"agent_actions":{"view_html":"https://pith.science/pith/Y6N5NIFGXMTWUZA6ESKVKVZCLV","download_json":"https://pith.science/pith/Y6N5NIFGXMTWUZA6ESKVKVZCLV.json","view_paper":"https://pith.science/paper/Y6N5NIFG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.0813&json=true","fetch_graph":"https://pith.science/api/pith-number/Y6N5NIFGXMTWUZA6ESKVKVZCLV/graph.json","fetch_events":"https://pith.science/api/pith-number/Y6N5NIFGXMTWUZA6ESKVKVZCLV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y6N5NIFGXMTWUZA6ESKVKVZCLV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y6N5NIFGXMTWUZA6ESKVKVZCLV/action/storage_attestation","attest_author":"https://pith.science/pith/Y6N5NIFGXMTWUZA6ESKVKVZCLV/action/author_attestation","sign_citation":"https://pith.science/pith/Y6N5NIFGXMTWUZA6ESKVKVZCLV/action/citation_signature","submit_replication":"https://pith.science/pith/Y6N5NIFGXMTWUZA6ESKVKVZCLV/action/replication_record"}},"created_at":"2026-05-18T02:02:08.961517+00:00","updated_at":"2026-05-18T02:02:08.961517+00:00"}