J. Korean Math. Soc. 2003; 40(3): 461-486
Printed May 1, 2003
Copyright © The Korean Mathematical Society.
Gerd Schmalz and Andrea Spiro
Friederich-Wilhelms-Universit\"at and Universit\`a di Camerino
It is known that the CR geometries of Levi non-degen-erate hypersurfaces in $\mathbb C^n$ and of the elliptic or hyperbolic CR submanifolds of codimension two in $\mathbb C^4$ 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 $f \in {\rm Aut}(M)_o \subset {\rm Aut}(M)$, $o \in M$, 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.
Keywords: CR structures, Chern-Moser bundle, normal coordinates
MSC numbers: Primary 32V05; Secondary 32V40
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