{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:LHR5THB34XBB27X3W5LD5QS27Z","short_pith_number":"pith:LHR5THB3","schema_version":"1.0","canonical_sha256":"59e3d99c3be5c21d7efbb7563ec25afe782dde6e249572330e484bc780f3294a","source":{"kind":"arxiv","id":"1109.6607","version":2},"attestation_state":"computed","paper":{"title":"D'atri spaces of type k and related classes of geometries concerning jacobi operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Maria J. Druetta, Teresa Arias-Marco","submitted_at":"2011-09-29T18:05:20Z","abstract_excerpt":"In this article we continue the study of the geometry of $k$-D'Atri spaces, $% 1\\leq k$ $\\leq n-1$ ($n$ denotes the dimension of the manifold)$,$ began by the second author. It is known that $k$-D'Atri spaces, $k\\geq 1,$ are related to properties of Jacobi operators $R_{v}$ along geodesics, since she has shown that ${\\operatorname{tr}}R_{v}$, ${\\operatorname{tr}}R_{v}^{2}$ are invariant under the geodesic flow for any unit tangent vector $v$. Here, assuming that the Riemannian manifold is a D'Atri space, we prove in our main result that ${\\operatorname{tr}}R_{v}^{3}$ is also invariant under th"},"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":"1109.6607","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-29T18:05:20Z","cross_cats_sorted":[],"title_canon_sha256":"73c1db26d5ece70edb56baea8b7f4c3015206dc40373d9b7303f4aba448d8743","abstract_canon_sha256":"7ed2688e54ae2861bb327c1bb8e5beaaa641693c35a5986434d8e3344034fc5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:14.675965Z","signature_b64":"Kv7p71IcsYLfB2pmF62CJpTj+UFRZltjPhmXwtIUyKjhB9jDPRphx15ck9lhuEguV6LhtX5XEixQL8Rx/dxjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59e3d99c3be5c21d7efbb7563ec25afe782dde6e249572330e484bc780f3294a","last_reissued_at":"2026-05-18T03:10:14.675458Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:14.675458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"D'atri spaces of type k and related classes of geometries concerning jacobi operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Maria J. Druetta, Teresa Arias-Marco","submitted_at":"2011-09-29T18:05:20Z","abstract_excerpt":"In this article we continue the study of the geometry of $k$-D'Atri spaces, $% 1\\leq k$ $\\leq n-1$ ($n$ denotes the dimension of the manifold)$,$ began by the second author. It is known that $k$-D'Atri spaces, $k\\geq 1,$ are related to properties of Jacobi operators $R_{v}$ along geodesics, since she has shown that ${\\operatorname{tr}}R_{v}$, ${\\operatorname{tr}}R_{v}^{2}$ are invariant under the geodesic flow for any unit tangent vector $v$. Here, assuming that the Riemannian manifold is a D'Atri space, we prove in our main result that ${\\operatorname{tr}}R_{v}^{3}$ is also invariant under th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6607","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":"1109.6607","created_at":"2026-05-18T03:10:14.675536+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.6607v2","created_at":"2026-05-18T03:10:14.675536+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6607","created_at":"2026-05-18T03:10:14.675536+00:00"},{"alias_kind":"pith_short_12","alias_value":"LHR5THB34XBB","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"LHR5THB34XBB27X3","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"LHR5THB3","created_at":"2026-05-18T12:26:34.985390+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/LHR5THB34XBB27X3W5LD5QS27Z","json":"https://pith.science/pith/LHR5THB34XBB27X3W5LD5QS27Z.json","graph_json":"https://pith.science/api/pith-number/LHR5THB34XBB27X3W5LD5QS27Z/graph.json","events_json":"https://pith.science/api/pith-number/LHR5THB34XBB27X3W5LD5QS27Z/events.json","paper":"https://pith.science/paper/LHR5THB3"},"agent_actions":{"view_html":"https://pith.science/pith/LHR5THB34XBB27X3W5LD5QS27Z","download_json":"https://pith.science/pith/LHR5THB34XBB27X3W5LD5QS27Z.json","view_paper":"https://pith.science/paper/LHR5THB3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.6607&json=true","fetch_graph":"https://pith.science/api/pith-number/LHR5THB34XBB27X3W5LD5QS27Z/graph.json","fetch_events":"https://pith.science/api/pith-number/LHR5THB34XBB27X3W5LD5QS27Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LHR5THB34XBB27X3W5LD5QS27Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LHR5THB34XBB27X3W5LD5QS27Z/action/storage_attestation","attest_author":"https://pith.science/pith/LHR5THB34XBB27X3W5LD5QS27Z/action/author_attestation","sign_citation":"https://pith.science/pith/LHR5THB34XBB27X3W5LD5QS27Z/action/citation_signature","submit_replication":"https://pith.science/pith/LHR5THB34XBB27X3W5LD5QS27Z/action/replication_record"}},"created_at":"2026-05-18T03:10:14.675536+00:00","updated_at":"2026-05-18T03:10:14.675536+00:00"}