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October, 2001 Equivalences of Real Submanifolds in Complex Space
M.S. Baouendi, Linda Preiss Rothschild, Dmitri Zaitsev
J. Differential Geom. 59(2): 301-351 (October, 2001). DOI: 10.4310/jdg/1090349430

Abstract

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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M.S. Baouendi. Linda Preiss Rothschild. Dmitri Zaitsev. "Equivalences of Real Submanifolds in Complex Space." J. Differential Geom. 59 (2) 301 - 351, October, 2001. https://doi.org/10.4310/jdg/1090349430

Information

Published: October, 2001
First available in Project Euclid: 20 July 2004

zbMATH: 1037.32030
MathSciNet: MR1908985
Digital Object Identifier: 10.4310/jdg/1090349430

Rights: Copyright © 2001 Lehigh University

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Vol.59 • No. 2 • October, 2001
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