{"paper":{"title":"Invariants and Umbilical Points on Three Dimensional CR Manifolds embedded in $\\mathbb C^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Dmitry Zaitsev, Peter Ebenfelt","submitted_at":"2016-05-27T16:25:05Z","abstract_excerpt":"We introduce a new sequence of CR invariant determinants on a three dimensional CR manifold $M$ embedded in $\\mathbb C^2$. The lowest order invariant $\\det A_3$ represents E. Cartan's 6th order invariant (the umbilical \"tensor\"), whose zero locus yields the set of umbilical points on $M$. As an application of this new presentation of the umbilical invariant, we show that generic, almost circular perturbations of the unit sphere always contain curves or surfaces of umbilical points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08709","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"}