{"paper":{"title":"Geodesic mapping onto K\\\"ahlerian space of the first kind","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Necessary and sufficient conditions for geodesic mappings from generalized Riemannian spaces onto generalized Kählerian spaces of the first kind are derived using a non-symmetric metric tensor.","cross_cats":[],"primary_cat":"math.DG","authors_text":"Irena Hinterleitner, Marija Najdanovi\\'c, Milan Zlatanovi\\'c","submitted_at":"2013-05-16T12:14:59Z","abstract_excerpt":"In the present paper a generalized K\\\"ahlerian space $\\mathbb{G}\\underset 1 {\\mathbb{K}}{}_N$ of the first kind is considered, as a generalized Riemannian space $\\mathbb{GR}_N$ with almost complex structure $F^h_i$, that is covariantly constant with respect to the first kind of covariant derivative.\n  Using the non-symmetric metric tensor we find necessary and sufficient conditions for a geodesic mapping $f:\\mathbb{GR}_N\\to \\mathbb{G}\\underset 1 {\\mathbb{\\bar{K}}}{}_N$ with respect to the four kinds of covariant derivatives."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Using the non-symmetric metric tensor we find necessary and sufficient conditions for a geodesic mapping f:GR_N → G K-bar_N with respect to the four kinds of covariant derivatives.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The almost complex structure F is covariantly constant with respect to the first kind of covariant derivative in the generalized Kählerian space of the first kind.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Necessary and sufficient conditions are found for geodesic mappings onto generalized Kählerian spaces of the first kind with respect to four covariant derivatives.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Necessary and sufficient conditions for geodesic mappings from generalized Riemannian spaces onto generalized Kählerian spaces of the first kind are derived using a non-symmetric metric tensor.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ea443556deee3266b56a31effe1c4f6406bff4d7e9694864dc6f04b29d9d3aab"},"source":{"id":"1305.3776","kind":"arxiv","version":1},"verdict":{"id":"3c184c7b-ae72-4454-9e8f-abd8954c8bb6","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T22:21:40.736756Z","strongest_claim":"Using the non-symmetric metric tensor we find necessary and sufficient conditions for a geodesic mapping f:GR_N → G K-bar_N with respect to the four kinds of covariant derivatives.","one_line_summary":"Necessary and sufficient conditions are found for geodesic mappings onto generalized Kählerian spaces of the first kind with respect to four covariant derivatives.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The almost complex structure F is covariantly constant with respect to the first kind of covariant derivative in the generalized Kählerian space of the first kind.","pith_extraction_headline":"Necessary and sufficient conditions for geodesic mappings from generalized Riemannian spaces onto generalized Kählerian spaces of the first kind are derived using a non-symmetric metric tensor."},"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"}