Journal of Differential Geometry

Equivalences of Real Submanifolds in Complex Space

M.S. Baouendi, Linda Preiss Rothschild, and Dmitri Zaitsev

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We show that for any real-analytic submanifold M in ℂN there is a proper real-analytic subvariety VM such that for any pM \ V, any realanalytic submanifold M in ℂN, and any pM, 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 pM \ 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.

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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.

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