{"paper":{"title":"Differential $\\{e\\}$-structures for equivalences of $2$-nondegenerate Levi rank $1$ hypersurfaces $M^5 \\subset \\mathbb{C}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Joel Merker (LM-Orsay), Wei Guo Foo (AMSS)","submitted_at":"2019-01-07T19:20:51Z","abstract_excerpt":"The class ${\\sf IV}_2$ of $2$-nondegenerate constant Levi rank $1$ hypersurfaces $M^5 \\subset \\mathbb{C}^3$ is governed by Pocchiola's two primary invariants $W_0$ and $J_0$. Their vanishing characterizes equivalence of such a hypersurface $M^5$ to the tube $M_{\\sf LC}^5$ over the real light cone in $\\mathbb{R}^3$. When either $W_0 \\not\\equiv 0$ or $J_0 \\not\\equiv 0$, by normalization of certain two group parameters ${\\sf c}$ and ${\\sf e}$, an invariant coframe can be built on $M^5$, showing that the dimension of the CR automorphism group drops from $10$ to $5$.\n  This paper constructs an expl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02028","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"}