{"paper":{"title":"Euclidean Hypersurfaces with Genuine Conformal Deformations in Codimension Two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ruy Tojeiro, Sergio Chion","submitted_at":"2018-05-17T19:14:19Z","abstract_excerpt":"In this paper we classify Euclidean hypersurfaces $f\\colon M^n \\rightarrow \\mathbb{R}^{n+1}$ with a principal curvature of multiplicity $n-2$ that admit a genuine conformal deformation $\\tilde{f}\\colon M^n \\rightarrow \\mathbb{R}^{n+2}$. That $\\tilde{f}\\colon M^n \\rightarrow \\mathbb{R}^{n+2}$ is a genuine conformal deformation of $f$ means that it is a conformal immersion for which there exists no open subset $U \\subset M^n$ such that the restriction $\\tilde{f}|_U$ is a composition $\\tilde f|_U=h\\circ f|_U$ of $f|_U$ with a conformal immersion $h\\colon V\\to \\mathbb{R}^{n+2}$ of an open subset $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06937","kind":"arxiv","version":1},"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"}