Equivalences of real submanifolds in complex space.
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Citation:Baouendi, M. S.; Rothschild, Linda Preiss; Zaitsev, Dmitri 'Equivalences of real submanifolds in complex space' in Journal of Differential Geometry, 59, (2), 2001, pp 301 - 351
We show that for any real-analytic submanifold M in CN there is a proper real-analytic subvariety V contained in M such that for any p ? M \ V , any real-analytic submanifold M? in CN, and any p? ? 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.
Keywords:Pure & Applied Mathematics
Series/Report no:Journal of Differential Geometry