Equivalences of real submanifolds in complex space.

Article English OPEN
ZAITSEV, DMITRI (2001)
  • Publisher: International Press
  • Subject: Pure & Applied Mathematics
    arxiv: Mathematics::Differential Geometry | Mathematics::Complex Variables | Mathematics::Symplectic Geometry

PUBLISHED 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.
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