{"paper":{"title":"Generic conformally flat hypersurfaces in $\\mathbb{R}^4$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Tongzhu Li, Xiu Ji","submitted_at":"2017-09-06T02:55:04Z","abstract_excerpt":"In this paper, we study generic conformally flat hypersurfaces in the Euclidean $4$-space $\\mathbb{R}^4$ using the framework of M\\\"{o}bius geometry. First, we classify locally the generic conformally flat hypersurfaces with closed M\\\"obius form under the M\\\"obius transformation group of $\\mathbb{R}^4$. Such examples come from cones, cylinders, or rotational hypersurfaces over the surfaces with constant Gaussian curvature in $3$-spheres, Euclidean $3$-spaces, or hyperbolic $3$-spaces, respectively. Second, we investigate the global behavior of the generic conformally flat hypersurface and give "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01657","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"}