{"paper":{"title":"Parallel Transport Frame in 4-dimensional Euclidean Space","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Fatma G\\\"ok\\c{c}el\\.ik, F. Nejat Ekmekc\\.i, \\.Ismail G\\\"ok, Yusuf Yayli, Zehra Bozkurt","submitted_at":"2012-07-12T15:31:32Z","abstract_excerpt":"In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the first time in 4-dimensional Euclidean space. Then we obtain the condition for spherical curves using the parallel transport frame of them. The condition in terms of \\kappa and {\\tau} is so complicated but in terms of k_{1} and k_{2} is simple. So, parallel transport frame is important to make easy some complicated characterizations. Moreover, we char"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2999","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"}