NORMAL SYSTEMS OF COORDINATES ON MANIFOLDS OF CHERN-MOSER TYPE

Title & Authors
NORMAL SYSTEMS OF COORDINATES ON MANIFOLDS OF CHERN-MOSER TYPE
Schmalz, Gerd; Spiro, Andrea;

Abstract
It is known that the CR geometries of Levi non-degen-erate hypersurfaces in $\small{\C^n}$ and of the elliptic or hyperbolic CR submanifolds of codimension two in $\small{\C^4}$ 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 $\small{f{\in}Aut(M)_o {\subset}Aut(M),\;o{\in}M}$, 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.
Keywords
CR structures;Chern-Moser bundle;normal coordinates;
Language
English
Cited by
1.
The Equivalence Problem for Five-dimensional Levi Degenerate CR Manifolds, International Mathematics Research Notices, 2014, 2014, 20, 5602
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