Equivalences of real submanifolds in complex space.

Abstract

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.