2019/01/07 by Wei Guo Foo, Foo, Wei Guo, Joël Merker +2
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #math.DG
paper · pdf · doi:10.48550/arxiv.1901.02028
71 pages, including an addendum shared with Samuel Pocchiola. Computations all done by hand -- zero computer help
arxiv created 2019/01/07 · openalex publication_date 2019/01/07 · arxiv updated 2019/01/09 · openalex created_date 2019/01/25 · openalex updated_date 2026/07/28
The class \sf IV2 of 2-nondegenerate constant Levi rank 1 hypersurfaces M5 ⊂ ℂ3 is governed by Pocchiola's two primary invariants W0 and J0. Their vanishing characterizes equivalence of such a hypersurface M5 to the tube M\sf LC5 over the real light cone in ℝ3. When either W0 \not≡ 0 or J0 \not≡ 0, by normalization of certain two group parameters \sf c and \sf e, an invariant coframe can be built on M5, showing that the dimension of the CR automorphism group drops from 10 to 5. This paper constructs an explicit \e\-structure in case W0 and J0 do not necessarily vanish. Furthermore, Pocchiola's calculations hidden on a computer now appear in details, especially the determination of a secondary invariant R, expressed in terms of the first jet of W0. All other secondary invariants of the \e\-structure are also expressed explicitly in terms of W0 and J0.