Equivalences of real submanifolds in complex space.
- Publisher: International Press
Pure & Applied Mathematics
arxiv: Mathematics::Differential Geometry | Mathematics::Complex Variables | Mathematics::Symplectic Geometry
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.