Normal form and two-dimensional chains of an elliptic CR manifold in \(\mathbb{C}^4\)
Let \(M\) be real-analytic CR manifold of codimension 2 in \(\mathbb{C}^4\) with elliptic form, passing through the origin. In analogy with the Chern-Moser normal form of a hypersurface, a construction of the normal form for \(M\) is given in this paper. Furthermore, it is shown that there exist as many such normal forms at a fixed point as there are isotropic automorphisms of the tangent elliptic quadric (Theorem 2). Also the authors prove that the chain-preserving normaliztions of a hypersurface, given in that normal form, must be a fractional linear transformation (Theorem 3).
elliptic CR manifold in \(\mathbb{C}^4\)
scientific article; zbMATH DE number 1191282