{"paper":{"title":"f-Eikonal helix submanifolds and f-Eikonal helix curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ali Senol, Evren Ziplar, Yusuf Yayli","submitted_at":"2012-06-02T18:03:21Z","abstract_excerpt":"Let M{\\subset}\\mathbb{R}^{n} be a Riemannian helix submanifold with respect to the unit direction d{\\in}\\mathbb{R}^{n} and f:M{\\to}\\mathbb{R} be a eikonal function. We say that M is a f-eikonal helix submanifold if for each q{\\in}M the angle between {\\nabla}f and d is constant.Let M{\\subset}\\mathbb{R}^{n} be a Riemannian submanifold and {\\alpha}:I{\\to}M be a curve with unit tangent T. Let f:M{\\to}\\mathbb{R} be a eikonal function along the curve {\\alpha}. We say that {\\alpha} is a f-eikonal helix curve if the angle between {\\nabla}f and T is constant along the curve {\\alpha}. {\\nabla}f will be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0395","kind":"arxiv","version":8},"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"}