Cartan equivalences for Levi-nondegenerate hypersurfaces M³ in C² belonging to General Class I

الأصل · EN

We develope in great computational details the classical Cartan equivalence problem for Levi-nondegenerate C⁶-smooth real hypersurfaces M³ in C², performing all calculations effectively in terms of a (local) graphing function φ. In particular, we present explicitly the unique (complex) essential invariant J of the problem. Its expansion in terms of the 3-variables function φincorporates millions of differential monomials, while, when φis assumed to depend only on 2 variables (rigid case), J writes out in two lines (7 monomials).