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HOME > Table of Contents and Abstracts > Vol. 66, No. 1
Tohoku Mathematical Journal
2014
March
SECOND SERIES VOL. 66, NO. 1
Tohoku Math. J.
66 (2014), 93-105
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Title
A PARAMETRIZED DE RHAM DECOMPOSITION THEOREM FOR CR MANIFOLDS
Author
Atsushi Hayashimoto
(Received June 11, 2012, revised May 9, 2013) |
Abstract.
The CR equivalence problem between CR manifolds with slice structure is studied. Let $N$ be a connected holomorphically nondegenerate real analytic hypersurface and $M(p)$ a finitely nondegenerate real analytic hypersurface parametrized by $p \in N$. Let $M$ be a totality of $N$ and $M(p)$ with moving $p$ in $N$. Assume that $M$ and $\widetilde{M}$ (with a same structure as $M$) are CR equivalent and that $N$ and $\widetilde{N}$ are also CR equivalent. Then we prove that, for any $p \in N$, there exists $\tilde{p}\in \widetilde{N}$ such that $M(p)$ is CR equivalent to $\widetilde{M}(\tilde{p})$.
Mathematics Subject Classification.
Primary 32V20; Secondary 32V35.
Key words and phrases.
CR equivalence, Segre mapping, finite nondegeneracy, holomorphic nondegeneracy.
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