Normal Systems of Coordinates on Manifolds of Chern-Moser Type

It is known that the CR geometries of Levi non-degenerate hyper-surfaces Cⁿ and of the elliptic or hyperbolic CR sub-manifolds of co-dimension two in C⁴ 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... 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.