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This class of relatively normalized ruled surfaces contains surfaces such that their relative image $\\varPhi^{*}$ is either a curve or it is as well as $\\varPhi$ a ruled surface whose generators are, additionally, parallel to those of $\\varPhi$. Moreover we inve"},"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":"1706.07277","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-21T15:17:56Z","cross_cats_sorted":[],"title_canon_sha256":"64d50946900e6f9ecf73d2daddae35ab7907b9a51be4c8172b837ada6c7f364a","abstract_canon_sha256":"cc4bb922e64e17dbbeb1f3300c0b8d9cc2efa8143ba18e936821fea3ad6b749a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:52.136241Z","signature_b64":"9gMO5hXm2eQTqTH7tBuwCyxJT6S6OjA3GmBybPWE5I8WBh8ZMxDatC9EEb5THkvvciLtxj1YZdw4mHqNWvViAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01fa33b8b2267c80c0f57d3ab6cc57490b48878dce580c0e4301aba92f53bd2a","last_reissued_at":"2026-05-18T00:41:52.135726Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:52.135726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ruled surfaces right normalized","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ioanna-Iris Papadopoulou, Stylianos Stamatakis","submitted_at":"2017-06-21T15:17:56Z","abstract_excerpt":"This paper deals with skew ruled surfaces $\\varPhi$ in the Euclidean space $\\mathbb{E}^{3}$ which are right normalized, that is they are equipped with relative normalizations, whose support function is of the form $q(u,v) = \\frac{f(u) + g(u)\\, v}{w(u,v)}$, where $w^2(u,v)$ is the discriminant of the first fundamental form of $\\varPhi$. This class of relatively normalized ruled surfaces contains surfaces such that their relative image $\\varPhi^{*}$ is either a curve or it is as well as $\\varPhi$ a ruled surface whose generators are, additionally, parallel to those of $\\varPhi$. 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