{"paper":{"title":"Euclidean hypersurfaces with genuine deformations in codimension two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Luis Florit, Marcos Dajczer, Ruy Tojeiro","submitted_at":"2010-10-14T14:22:33Z","abstract_excerpt":"We classify hypersurfaces of rank two of Euclidean space $\\R^{n+1}$ that admit genuine isometric deformations in $\\R^{n+2}$. That an isometric immersion $\\hat f\\colon\\,M^n\\to\\R^{n+2}$ is a genuine isometric deformation of a hypersurface $f\\colon\\, M^n\\to\\R^{n+1}$ means that $\\hat f$ is nowhere a composition $\\hat f=\\hat F\\circ f$, where $\\hat F\\colon\\,V\\subset \\R^{n+1}\\to\\R^{n+2}$ is an isometric immersion of an open subset $V$ containing $f(M)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2932","kind":"arxiv","version":2},"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"}