Normal systems of coordinates on manifolds of Chern-Moser type

Abstract

It is known that the CR geometries of Levi non-degen-erate hypersurfaces in $\C^n$ and of the elliptic or hyperbolic CR submanifolds of codimension two in $\C^4$ share many common features. In this paper, a special class of normalized coordinates is introduced for any CR manifold $M$ which is one of the above three kinds and it is shown that the explicit expression in these coordinates of an isotropy automorphism $f \in \Aut(M)_o \subset \Aut(M)$, $o \in M$, is equal to the expression of a corresponding element of the automorphism group of the homogeneous model. As an application of this property, an extension theorem for CR maps is obtained.