{"paper":{"title":"Normal forms for CR singular codimension two Levi-flat submanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jiri Lebl, Xianghong Gong","submitted_at":"2014-03-03T20:29:50Z","abstract_excerpt":"Real-analytic Levi-flat codimension two CR singular submanifolds are a natural generalization to ${\\mathbb{C}}^m$, $m > 2$, of Bishop surfaces in ${\\mathbb{C}}^2$. Such submanifolds for example arise as zero sets of mixed-holomorphic equations with one variable antiholomorphic. We classify the codimension two Levi-flat CR singular quadrics, and we notice that new types of submanifolds arise in dimension 3 or greater. In fact, the nondegenerate submanifolds, i.e. higher order purturbations of $z_m=\\bar{z}_1z_2+\\bar{z}_1^2$, have no analogue in dimension 2. We prove that the Levi-foliation exten"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0558","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"}