{"paper":{"title":"On Inclined Curves According to Parallel Transport Frame in E4","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","submitted_at":"2013-03-29T15:28:00Z","abstract_excerpt":"In this paper, we introduce an inclined curves according to parallel transport frame. Also, we define a vector field called Darboux vector field of an inclined curve in and we give a new characterization such as: \"\\alpha: I \\subset R \\rightarrow E^4 is an inclined curve \\Leftrightarrow k_1 \\int k_1ds + k_2 \\int \\k_2 +k_3ds = 0\" where k_1, k_2, K_3 are the principal curvature functions according to parallel transport frame of the curve and we give the similar characterizations such as \"\\alpha : I \\subset R \\rightarrow E^3 is a generalized helix \\Leftrightarrow k_1 \\int k_1ds + k_2 \\int k_2ds = "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7422","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"}