Projection on Segre varieties and determination of holomorphic mappings between real submanifolds
M. S. Baouendi, Peter Ebenfelt, Linda P. Rothschild
Abstract
It is shown that a germ of a holomorphic mapping sending a real-analytic generic submanifold of finite type into another is determined by its projection on the Segre variety of the target manifold. A necessary and sufficient condition is given for a germ of a mapping into the Segre variety of the target manifold to be the projection of a holomorphic mapping sending the source manifold into the target. An application to the biholomorphic equivalence problem is also given.
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