{"paper":{"title":"On Mannheim Partner Curves in three Dimensional Lie Groups","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"\\.Ismail G\\\"ok, Nejat Ekmekci, O. Zeki Okuyucu, Yusuf Yayl{\\i}","submitted_at":"2012-11-26T21:38:52Z","abstract_excerpt":"In this paper, we define Mannheim partner curves in a three dimensional Lie group G with a bi-invariant metric. And then the main result in this paper is given as (Theorem 3.3): A curve {\\alpha} with the Frenet apparatus {T,N,B,{\\kappa},{\\tau}} in G is a Mannheim partner curve if and only if {\\lambda}{\\kappa}(1+H2)=1, where {\\lambda} is constant and H is the harmonic curvature function of the curve {\\alpha}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6141","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"}