{"paper":{"title":"Second-order equations and local isometric immersions of pseudo-spherical surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Keti Tenenblat, Nabil Kahouadji, Niky Kamran","submitted_at":"2013-08-29T18:24:05Z","abstract_excerpt":"We consider the class of differential equations that describe pseudo-spherical surfaces of the form  $u\\_t=F(u,u\\_x,u\\_{xx})$ and $u\\_{xt}=F(u, u\\_x)$ given in Chern-Tenenblat \\cite{ChernTenenblat} and Rabelo-Tenenblat \\cite{RabeloTenenblat90}.  We answer the following question: Given a pseudo-spherical surface determined by a solution $u$ of such an equation, do the coefficients of the second fundamental form of the local isometric immersion in $\\mathbb{R}^3$ depend on a jet of finite order of $u$? We show that, except for the sine-Gordon equation, where the coefficients  depend on a jet of o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6545","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"}