Journal of Differential Geometry
- J. Differential Geom.
- Volume 59, Number 2 (2001), 301-351.
Equivalences of Real Submanifolds in Complex Space
We show that for any real-analytic submanifold M in ℂN there is a proper real-analytic subvariety V ⊂ M such that for any p ∊ M \ V, any realanalytic submanifold M′ in ℂN, and any p′ ∊ M′, the germs (M, p) and (M′, p′) of the submanifolds M and M′ at p and p′ respectively are formally equivalent if and only if they are biholomorphically equivalent. As an application, for p ∊ M \ V, the problem of biholomorphic equivalence of the germs (M, p) and (M′, p′) is reduced to that of solving a system of polynomial equations. More general results for k-equivalences are also stated and proved.
J. Differential Geom., Volume 59, Number 2 (2001), 301-351.
First available in Project Euclid: 20 July 2004
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Baouendi, M.S.; Rothschild, Linda Preiss; Zaitsev, Dmitri. Equivalences of Real Submanifolds in Complex Space. J. Differential Geom. 59 (2001), no. 2, 301--351. doi:10.4310/jdg/1090349430. https://projecteuclid.org/euclid.jdg/1090349430