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Equivalences of real submanifolds in complex space

M. S. Baouendi·Linda Preiss Rothschild·Dmitri Zaitsev
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Abstract

We show that for any real-analytic submanifold M in C^N there is a proper real-analytic subvariety V contained in M such that for any point p in M\V, any real-analytic submanifold M' in C^N, and any point p' in M', the germs of the submanifolds M and M' at p and p' respectively are formally equivalent if and only if they are biholomorphically equivalent. More general results for k-equivalences are also stated and proved.

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M. S. Baouendi, Linda Preiss Rothschild, Dmitri Zaitsev. 2000-02-22. Equivalences of real submanifolds in complex space. https://arxiv.org/abs/math/0002186

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