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We give a non-existence result for general canal surfaces in E^3 with vanishing the curvatures K, H, K_{II} and H_{II} except the cylinder and cone.We classify the general canal surfaces for which are degenerate according to their radiuses. Finally we obtain that there are no flat, minimal, II-flat and II-minimal general canal surfaces in the"},"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":"1106.3177","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-06-16T09:07:45Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"3662a44a61208aab9b51281d65a939da5313861a782be2d069ef1751a4d06578","abstract_canon_sha256":"b9efb8868cf9f6c506f4c8b08e7c341ac8f195cbe7eaa96c2bc330a870651aed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:15.690590Z","signature_b64":"IkFBxxMHqVJLY/l8tNvht9B4K7LKK3Zf+/0DVderHJbCfV4kRy3Aw3d12PLKkdtToUaAdrVHOUsqtb35TfOnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f2090cd7db4cd57c694853831ba0d830236259281c030bb3dd5e0204defd531","last_reissued_at":"2026-05-18T01:15:15.689861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:15.689861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On geometry of the first and second fundamental forms of canal surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.DG","authors_text":"Y{\\i}lmaz Tun\\c{c}er","submitted_at":"2011-06-16T09:07:45Z","abstract_excerpt":"In this study, we analyze the general canal surfaces in terms of the features flat, II-flat minimality and II-minimality, namely we study under which conditions the first and second Gauss and mean curvature vanishes, i.e. K=0, H=0, K_{II}=0 and H_{II} =0. We give a non-existence result for general canal surfaces in E^3 with vanishing the curvatures K, H, K_{II} and H_{II} except the cylinder and cone.We classify the general canal surfaces for which are degenerate according to their radiuses. 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