{"paper":{"title":"Biharmonic hypersurfaces in a conformally flat space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Liang Tang, Ye-Lin Ou","submitted_at":"2012-04-25T03:07:29Z","abstract_excerpt":"Biharmonic hypersurfaces in a generic conformally flat space are studied in this paper. The equation of such hypersurfaces is derived and is used to determine the conformally flat metric $f^{-2}\\delta_{ij}$ on the Euclidean space $\\mathbb{R}^{m+1}$ so that a minimal hypersurface $M^m\\longrightarrow (\\mathbb{R}^{m+1}, \\delta_{ij})$ in a Euclidean space becomes a biharmonic hypersurface $M^m\\longrightarrow (\\mathbb{R}^{m+1}, f^{-2}\\delta_{ij})$ in the conformally flat space. Our examples include all biharmonic hypersurfaces found in [Ou1] and [OT] as special cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5550","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"}