Geodesic
The Cartan equivalence problem for Levi-non-degenerate real hypersurfaces $M^3\subset\mathbb C^2$
Izvestiya. Mathematics , Tome 78 (2014) no. 6, pp. 1158-1194

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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.
Keywords: CR-manifolds, Levi non-degeneracy, curvature tensor.
Mots-clés : essential torsions, $G$-structures 
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     author = {J. Merker and M. Sabzevari},
     title = {The {Cartan} equivalence problem for {Levi-non-degenerate} real hypersurfaces $M^3\subset\mathbb C^2$},
     journal = {Izvestiya. Mathematics },
     pages = {1158--1194},
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     year = {2014},
     language = {en},
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J. Merker; M. Sabzevari. The Cartan equivalence problem for Levi-non-degenerate real hypersurfaces $M^3\subset\mathbb C^2$. Izvestiya. Mathematics , Tome 78 (2014) no. 6, pp. 1158-1194. http://geodesic.mathdoc.fr/item/IM2_2014_78_6_a6/