{"paper":{"title":"An example of non-embeddability of the Ricci flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mohammad Safdari","submitted_at":"2014-08-10T18:05:42Z","abstract_excerpt":"For an evolution of metrics $(M,g_{t})$ there is a t-smooth family of embeddings $e_{t}:M\\to\\mathbb{R}^{N}$ inducing $g_{t}$, but in general there is no family of embeddings extending a given initial embedding $e_{0}$. We give an example of this phenomenon when $g_{t}$ is the evolution of $g_{0}$ under the Ricci flow. We show that there are embeddings $e_{0}$ inducing $g_{0}$ which do not admit of t-smooth extensions to $e_{t}$ inducing $g_{t}$ for any t>0. We also find hypersurfaces of dim>2 that will not remain a hypersurface under Ricci flow for any positive time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2259","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"}