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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1206.0395","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-02T18:03:21Z","cross_cats_sorted":[],"title_canon_sha256":"f33e0bcd2280089160c2252a834db267842e7d82ce2e910fb7666aedf6700344","abstract_canon_sha256":"15699b251ca0ae75e87ba8bde409066a00880aec51efae5052ce0de8b9985ba2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:14.534262Z","signature_b64":"IHgoDU6mKY2hNpu7w5GeoNPbZv7uEM3skzGOl8S64yhuRrC+SRJCjAVxJxANr0Tj9tNouQN049hFdz1U6jvMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9a626f5e05ffbcdc88f6c1bf30d23e53aa353e34e745bfc8f4f879c1409e9ee","last_reissued_at":"2026-05-18T03:39:14.533725Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:14.533725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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