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 $\widetilde{M}(\tilde{p})$.
Citation
Atsushi Hayashimoto. "A parametrized de Rham decomposition theorem for CR manifolds." Tohoku Math. J. (2) 66 (1) 93 - 105, 2014. https://doi.org/10.2748/tmj/1396875664
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