{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:C5XK3OY46SGKL3URYNXU2MJHGH","short_pith_number":"pith:C5XK3OY4","schema_version":"1.0","canonical_sha256":"176eadbb1cf48ca5ee91c36f4d312731ffee58094036fd171c541cd28fcb4567","source":{"kind":"arxiv","id":"1011.5892","version":1},"attestation_state":"computed","paper":{"title":"Surfaces with parallel mean curvature vector in complex space forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dorel Fetcu","submitted_at":"2010-11-25T21:49:53Z","abstract_excerpt":"We consider a quadratic form defined on the surfaces with parallel mean curvature vector of an any dimensional complex space form and prove that its $(2,0)$-part is holomorphic. When the complex dimension of the ambient space is equal to $2$ we define a second quadratic form with the same property and then determine those surfaces with parallel mean curvature vector on which the $(2,0)$-parts of both of them vanish. We also provide a reduction of codimension theorem and prove a non-existence result for $2$-spheres with parallel mean curvature vector."},"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":"1011.5892","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-25T21:49:53Z","cross_cats_sorted":[],"title_canon_sha256":"e008c3f725d2a4ded5e4dd3140e28229c6a6bc238d1c9ce9247e6fec63971ce9","abstract_canon_sha256":"2738b4c747b7ef2aee2324473df6aeacccf9785637686ae2347b18dbfc8c98c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:37.946628Z","signature_b64":"HFhrGITIIYo/QlcTTPix7FcDTcUSotmPru7pDspXc2RKwqvZFdqIl/oVd9kP6xIt1xbTtOHh5mjya0XPZOVJCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"176eadbb1cf48ca5ee91c36f4d312731ffee58094036fd171c541cd28fcb4567","last_reissued_at":"2026-05-18T04:34:37.945893Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:37.945893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Surfaces with parallel mean curvature vector in complex space forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dorel Fetcu","submitted_at":"2010-11-25T21:49:53Z","abstract_excerpt":"We consider a quadratic form defined on the surfaces with parallel mean curvature vector of an any dimensional complex space form and prove that its $(2,0)$-part is holomorphic. When the complex dimension of the ambient space is equal to $2$ we define a second quadratic form with the same property and then determine those surfaces with parallel mean curvature vector on which the $(2,0)$-parts of both of them vanish. We also provide a reduction of codimension theorem and prove a non-existence result for $2$-spheres with parallel mean curvature vector."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5892","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":"1011.5892","created_at":"2026-05-18T04:34:37.946011+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.5892v1","created_at":"2026-05-18T04:34:37.946011+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5892","created_at":"2026-05-18T04:34:37.946011+00:00"},{"alias_kind":"pith_short_12","alias_value":"C5XK3OY46SGK","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"C5XK3OY46SGKL3UR","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"C5XK3OY4","created_at":"2026-05-18T12:26:05.355336+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/C5XK3OY46SGKL3URYNXU2MJHGH","json":"https://pith.science/pith/C5XK3OY46SGKL3URYNXU2MJHGH.json","graph_json":"https://pith.science/api/pith-number/C5XK3OY46SGKL3URYNXU2MJHGH/graph.json","events_json":"https://pith.science/api/pith-number/C5XK3OY46SGKL3URYNXU2MJHGH/events.json","paper":"https://pith.science/paper/C5XK3OY4"},"agent_actions":{"view_html":"https://pith.science/pith/C5XK3OY46SGKL3URYNXU2MJHGH","download_json":"https://pith.science/pith/C5XK3OY46SGKL3URYNXU2MJHGH.json","view_paper":"https://pith.science/paper/C5XK3OY4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.5892&json=true","fetch_graph":"https://pith.science/api/pith-number/C5XK3OY46SGKL3URYNXU2MJHGH/graph.json","fetch_events":"https://pith.science/api/pith-number/C5XK3OY46SGKL3URYNXU2MJHGH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C5XK3OY46SGKL3URYNXU2MJHGH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C5XK3OY46SGKL3URYNXU2MJHGH/action/storage_attestation","attest_author":"https://pith.science/pith/C5XK3OY46SGKL3URYNXU2MJHGH/action/author_attestation","sign_citation":"https://pith.science/pith/C5XK3OY46SGKL3URYNXU2MJHGH/action/citation_signature","submit_replication":"https://pith.science/pith/C5XK3OY46SGKL3URYNXU2MJHGH/action/replication_record"}},"created_at":"2026-05-18T04:34:37.946011+00:00","updated_at":"2026-05-18T04:34:37.946011+00:00"}