Rational dependence of smooth and analytic CR mappings on their jets

Details Rational dependence of smooth and analytic CR mappings on their jets Rational dependence of smooth and analytic CR mappings on their jets

1998-11-17

arxiv.org/abs/math/9811104v1

Mathematics

Complex Variables

AMS-TeX (amsppt); 38 pages

Scientific paper

We consider CR submersive mappings between generic submanifolds in complex space. We show that, under suitable conditions on the manifolds, there is an integer k such that any jet of the CR mapping at a given point is a rational function of its k-jet at that point. As a consequence, it is shown that the stability group of a (suitably nondegenerate) real-analytic generic submanifold is a real algebraic Lie group. Moreover, it is shown that a formal equivalence between two such real-analytic submanifolds is necessarily convergent.

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