{"paper":{"title":"Isometric Embedding and Darboux Integrability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Jeanne Clelland, Naghmana Tehseen, Peter Vassiliou, Thomas Ivey","submitted_at":"2017-12-31T05:55:30Z","abstract_excerpt":"Given a smooth 2-dimensional Riemannian or pseudo-Riemannian manifold $(M, \\boldsymbol{g})$ and an ambient 3-dimensional Riemannian or pseudo-Riemannian manifold $(N, \\boldsymbol{h})$, one can ask under what circumstances does the exterior differential system $\\mathcal{I}$ for the isometric embedding $M\\hookrightarrow N$ have particularly nice solvability properties. In this paper we give a classification of all $2$-metrics $\\boldsymbol{g}$ whose local isometric embedding system into flat Riemannian or pseudo-Riemannian 3-manifolds $(N, \\boldsymbol{h})$ is Darboux integrable. As an illustratio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00241","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"}