{"paper":{"title":"A new characterization of canal surfaces with parallel transport frame in Euclidean space $\\mathbb{E}^{4}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"G\\\"unay \\\"Ozt\\\"urk, \\.Ilim Ki\\c{s}i, Kadri Arslan","submitted_at":"2014-12-08T11:56:14Z","abstract_excerpt":"In this study, we consider canal surfaces according to parallel transport frame in Euclidean space $\\mathbb{E}^{4}$. The curvature properties of these surfaces are investigated with respect to $k_{1}$, $k_{2}$ and $k_{3}$ which are principal curvature functions according to parallel transport frame. We also give an example of canal surfaces in $\\mathbb{E}^{4}.$ Further, we point out that if spine curve $\\gamma $ is a straight line, then $M$ is a Weingarten canal surface and also $M$ is a linear Weingarten tube surface. Finally, the visualization of the projections of canal surfaces in $\\mathbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06947","kind":"arxiv","version":2},"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"}