{"paper":{"title":"On the dynamics of some vector fields tangent to non-integrable plane fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Nicola Pia","submitted_at":"2019-05-28T14:23:21Z","abstract_excerpt":"Let $\\mathcal{E}^3\\subset TM^n$ be a smooth $3$-distribution on a smooth manifold of dimension $n$ and $\\mathcal{W}\\subset\\mathcal{E}$ a line field such that $[\\mathcal{W},\\mathcal{E}]\\subset\\mathcal{E}$. Under some orientability hypothesis, we give a necessary condition for the existence of a plane field $\\mathcal{D}^2$ such that $\\mathcal{W}\\subset\\mathcal{D}$ and $[\\mathcal{D},\\mathcal{D}]=\\mathcal{E}$. Moreover we study the case where a section of $\\mathcal{W}$ is non-singular Morse-Smale and we get a sufficient condition for the global existence of $\\mathcal{D}$. As a corollary we get con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11839","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"}