Equivalences of real submanifolds in complex space

Baouendi, M. S.; Rothschild, Linda Preiss; Zaitsev, Dmitri

Equivalences of real submanifolds in complex space

Authors

Baouendi, M. S.

Rothschild, Linda Preiss

Zaitsev, Dmitri

Description

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.
38 pages, LateX