{"paper":{"title":"Timelike Bertrand Curves in Semi-Euclidean Space","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Murat Tosun, Soley Ersoy","submitted_at":"2010-03-05T09:50:29Z","abstract_excerpt":"In this paper, it is proved that, no special timelike Frenet curve is a Bertrand curve in $\\mathbb{E}_2^4$ and also, in $\\mathbb{E}_\\nu^{n+1}$ $ ({n \\ge 3})$, such that the notion of Bertrand curve is definite only in $\\mathbb{E}_1^2$ and $\\mathbb{E}_1^3$. Therefore, a generalization of timelike Bertrand curve is defined and called as timelike (1,3)-Bertrand curve in $\\mathbb{E}_2^4$. Moreover, the characterization of timelike (1,3)-Bertrand curve is given in $\\mathbb{E}_2^4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1220","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"}