{"paper":{"title":"Hypersurfaces of two space forms and conformally flat hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"R. Tojeiro, S. Canevari","submitted_at":"2015-08-11T15:30:37Z","abstract_excerpt":"We address the problem of determining the hypersurfaces $f\\colon M^{n} \\to \\mathbb{Q}_s^{n+1}(c)$ with dimension $n\\geq 3$ of a pseudo-Riemannian space form of dimension $n+1$, constant curvature $c$ and index $s\\in \\{0, 1\\}$ for which there exists another isometric immersion $\\tilde{f}\\colon M^{n} \\to \\mathbb{Q}^{n+1}_{\\tilde s}(\\tilde{c})$ with $\\tilde{c}\\neq c$. For $n\\geq 4$, we provide a complete solution by extending results for $s=0=\\tilde s$ by do Carmo and Dajczer and by Dajczer and the second author. Our main results are for the most interesting case $n=3$, and these are new even in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02628","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"}