The Cartan equivalence problem for Levi-non-degenerate real hypersurfaces M^3 in C^2

Joël Merker (1) , Masoud Sabzevari (2)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 Department of Pure Mathematics [Shahrekord]

We develop the Cartan equivalence problem for Levi-non- degenerate $\mathcal C^6$-smooth real hypersurfaces $M^3$ in $\mathbb C^2$ in great detail, performing all computations effectively in terms of local graphing functions. In particular, we present explicitly the unique (complex) essential invariant $\mathfrak{J}$ of the problem. Comparison with our previous joint results [1] shows that the Cartan–Tanaka geometry of these real hypersurfaces perfectly matches their biholomorphic equivalence.

Mots clés: CR-manifolds; Levi non-degeneracy; essential torsions; Gstructures; curvature tensor; CR-manifolds

Domaines: Mathématiques [math]

Joël Merker, Masoud Sabzevari. The Cartan equivalence problem for Levi-non-degenerate real hypersurfaces M^3 in C^2. Izvestiya: Mathematics, 2014, 78 (6), pp.1158-1194. ⟨10.1070/IM2014v078n06ABEH002725⟩. ⟨hal-03286249⟩