{"paper":{"title":"Exotic holomorphic Engel structures on C4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Nicola Pia, Rui Coelho","submitted_at":"2017-06-28T14:10:48Z","abstract_excerpt":"A holomorphic Engel structure determines a flag of distributions $\\mathcal{W}\\subset \\mathcal{D}\\subset \\mathcal{E}$. We construct examples of Engel structures on $\\mathbf{C}^4$ such that each of these distributions is hyperbolic in the sense that it has no tangent copies of $\\mathbf{C}$. We also construct two infinite families of pairwise non-isomorphic Engel structures on $\\mathbf{C}^4$ by controlling the curves $f:\\mathbf{C}\\to \\mathbf{C}^4$ tangent to $\\mathcal{W}$. The first is characterised by the topology of the set of points in $\\mathbf{C}^4$ admitting $\\mathcal{W}$-lines, and the seco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09306","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"}