{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YMEZE6SEZQDELDNX2GBLW4U2IU","short_pith_number":"pith:YMEZE6SE","schema_version":"1.0","canonical_sha256":"c309927a44cc06458db7d182bb729a45218ce3bd0ae0a34dfa80a12bf3b180bc","source":{"kind":"arxiv","id":"1407.2790","version":1},"attestation_state":"computed","paper":{"title":"Ricci solitons and concurrent vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bang-Yen Chen, Sharief Deshmukh","submitted_at":"2014-07-10T13:55:38Z","abstract_excerpt":"A Ricci soliton $(M^n,g,v,\\lambda)$ on a Riemannian manifold $(M^n,g)$ is said to have concurrent potential field if its potential field $v$ is a concurrent vector field.\n  In the first part of this paper we completely classify Ricci solitons with concurrent potential fields. In the second part we derive a necessary and sufficient condition for a submanifold to be a Ricci soliton in a Riemannian manifold equipped with a concurrent vector field. In the last part, we classify shrinking Ricci solitons with $\\lambda=1$ on Euclidean hypersurfaces.\n  Several applications of our results are also pres"},"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":"1407.2790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-10T13:55:38Z","cross_cats_sorted":[],"title_canon_sha256":"1cb5127e310f5760154263c5fbd69b5217964518dfbb30368b817f231736cfce","abstract_canon_sha256":"8866e663ed7de556e8cbd97889194b85b4bbd00cc63906c886b37d45a3839ee1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:53.652791Z","signature_b64":"G7hTHV73RfhnPjhZfwbpZcSR+jufsbiKjwAMX8g/QPjoJxRKaTeiL3Bu7YMsY6As6cQ21yPLHCVHkmwVkq80DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c309927a44cc06458db7d182bb729a45218ce3bd0ae0a34dfa80a12bf3b180bc","last_reissued_at":"2026-05-18T02:47:53.652312Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:53.652312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ricci solitons and concurrent vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bang-Yen Chen, Sharief Deshmukh","submitted_at":"2014-07-10T13:55:38Z","abstract_excerpt":"A Ricci soliton $(M^n,g,v,\\lambda)$ on a Riemannian manifold $(M^n,g)$ is said to have concurrent potential field if its potential field $v$ is a concurrent vector field.\n  In the first part of this paper we completely classify Ricci solitons with concurrent potential fields. In the second part we derive a necessary and sufficient condition for a submanifold to be a Ricci soliton in a Riemannian manifold equipped with a concurrent vector field. In the last part, we classify shrinking Ricci solitons with $\\lambda=1$ on Euclidean hypersurfaces.\n  Several applications of our results are also pres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2790","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":"1407.2790","created_at":"2026-05-18T02:47:53.652389+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.2790v1","created_at":"2026-05-18T02:47:53.652389+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2790","created_at":"2026-05-18T02:47:53.652389+00:00"},{"alias_kind":"pith_short_12","alias_value":"YMEZE6SEZQDE","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"YMEZE6SEZQDELDNX","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"YMEZE6SE","created_at":"2026-05-18T12:28:57.508820+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/YMEZE6SEZQDELDNX2GBLW4U2IU","json":"https://pith.science/pith/YMEZE6SEZQDELDNX2GBLW4U2IU.json","graph_json":"https://pith.science/api/pith-number/YMEZE6SEZQDELDNX2GBLW4U2IU/graph.json","events_json":"https://pith.science/api/pith-number/YMEZE6SEZQDELDNX2GBLW4U2IU/events.json","paper":"https://pith.science/paper/YMEZE6SE"},"agent_actions":{"view_html":"https://pith.science/pith/YMEZE6SEZQDELDNX2GBLW4U2IU","download_json":"https://pith.science/pith/YMEZE6SEZQDELDNX2GBLW4U2IU.json","view_paper":"https://pith.science/paper/YMEZE6SE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.2790&json=true","fetch_graph":"https://pith.science/api/pith-number/YMEZE6SEZQDELDNX2GBLW4U2IU/graph.json","fetch_events":"https://pith.science/api/pith-number/YMEZE6SEZQDELDNX2GBLW4U2IU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YMEZE6SEZQDELDNX2GBLW4U2IU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YMEZE6SEZQDELDNX2GBLW4U2IU/action/storage_attestation","attest_author":"https://pith.science/pith/YMEZE6SEZQDELDNX2GBLW4U2IU/action/author_attestation","sign_citation":"https://pith.science/pith/YMEZE6SEZQDELDNX2GBLW4U2IU/action/citation_signature","submit_replication":"https://pith.science/pith/YMEZE6SEZQDELDNX2GBLW4U2IU/action/replication_record"}},"created_at":"2026-05-18T02:47:53.652389+00:00","updated_at":"2026-05-18T02:47:53.652389+00:00"}