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Rational dependence of smooth and analytic CR mappings on their jets

M. S. Baouendi·P. Ebenfelt·Linda Preiss Rothschild
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Abstract

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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M. S. Baouendi, P. Ebenfelt, Linda Preiss Rothschild. 1998-11-17. Rational dependence of smooth and analytic CR mappings on their jets. https://arxiv.org/abs/math/9811104

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