{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:UIP2LSLHJLL36OM4NGMQUYBP3Q","short_pith_number":"pith:UIP2LSLH","schema_version":"1.0","canonical_sha256":"a21fa5c9674ad7bf399c69990a602fdc3b07d7c4892b4f7f93ca8b8d707e304a","source":{"kind":"arxiv","id":"1112.0779","version":1},"attestation_state":"computed","paper":{"title":"The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Alexander Petkov, Dimiter Vassilev, Srefan Ivanov","submitted_at":"2011-12-04T17:07:09Z","abstract_excerpt":"The main technical result of the paper is a Bochner type formula for the sub-laplacian on a quaternionic contact manifold. With the help of this formula we establish a version of Lichnerowicz' theorem giving a lower bound of the eigenvalues of the sub-Laplacian under a lower bound on the $Sp(n)Sp(1)$ components of the qc-Ricci curvature. It is shown that in the case of a 3-Sasakian manifold the lower bound is reached iff the quaternionic contact manifold is a round 3-Sasakian sphere. Another goal of the paper is to establish a-priori estimates for square integrals of horizontal derivatives of "},"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":"1112.0779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-04T17:07:09Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"41c747b4af876a78de1e606eb23170fc0ea075e8269acaa14895289455a95a08","abstract_canon_sha256":"3962e29ac2f3330f0448d38a8494df38e61835fba6f2b33101c6ef2d612edb32"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:05.647825Z","signature_b64":"cZTNM7jDPboGinnXz8ERDOxSJab2Lx+tjF6X9eRPMNnCvgcjHDSmVhnk9d8flffCwdutRo7LR/Klwd2AeCB0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a21fa5c9674ad7bf399c69990a602fdc3b07d7c4892b4f7f93ca8b8d707e304a","last_reissued_at":"2026-05-18T04:07:05.647193Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:05.647193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Alexander Petkov, Dimiter Vassilev, Srefan Ivanov","submitted_at":"2011-12-04T17:07:09Z","abstract_excerpt":"The main technical result of the paper is a Bochner type formula for the sub-laplacian on a quaternionic contact manifold. With the help of this formula we establish a version of Lichnerowicz' theorem giving a lower bound of the eigenvalues of the sub-Laplacian under a lower bound on the $Sp(n)Sp(1)$ components of the qc-Ricci curvature. It is shown that in the case of a 3-Sasakian manifold the lower bound is reached iff the quaternionic contact manifold is a round 3-Sasakian sphere. Another goal of the paper is to establish a-priori estimates for square integrals of horizontal derivatives of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0779","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":"1112.0779","created_at":"2026-05-18T04:07:05.647274+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.0779v1","created_at":"2026-05-18T04:07:05.647274+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0779","created_at":"2026-05-18T04:07:05.647274+00:00"},{"alias_kind":"pith_short_12","alias_value":"UIP2LSLHJLL3","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"UIP2LSLHJLL36OM4","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"UIP2LSLH","created_at":"2026-05-18T12:26:42.757692+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/UIP2LSLHJLL36OM4NGMQUYBP3Q","json":"https://pith.science/pith/UIP2LSLHJLL36OM4NGMQUYBP3Q.json","graph_json":"https://pith.science/api/pith-number/UIP2LSLHJLL36OM4NGMQUYBP3Q/graph.json","events_json":"https://pith.science/api/pith-number/UIP2LSLHJLL36OM4NGMQUYBP3Q/events.json","paper":"https://pith.science/paper/UIP2LSLH"},"agent_actions":{"view_html":"https://pith.science/pith/UIP2LSLHJLL36OM4NGMQUYBP3Q","download_json":"https://pith.science/pith/UIP2LSLHJLL36OM4NGMQUYBP3Q.json","view_paper":"https://pith.science/paper/UIP2LSLH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.0779&json=true","fetch_graph":"https://pith.science/api/pith-number/UIP2LSLHJLL36OM4NGMQUYBP3Q/graph.json","fetch_events":"https://pith.science/api/pith-number/UIP2LSLHJLL36OM4NGMQUYBP3Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UIP2LSLHJLL36OM4NGMQUYBP3Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UIP2LSLHJLL36OM4NGMQUYBP3Q/action/storage_attestation","attest_author":"https://pith.science/pith/UIP2LSLHJLL36OM4NGMQUYBP3Q/action/author_attestation","sign_citation":"https://pith.science/pith/UIP2LSLHJLL36OM4NGMQUYBP3Q/action/citation_signature","submit_replication":"https://pith.science/pith/UIP2LSLHJLL36OM4NGMQUYBP3Q/action/replication_record"}},"created_at":"2026-05-18T04:07:05.647274+00:00","updated_at":"2026-05-18T04:07:05.647274+00:00"}