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ON THE CLASSIFICATION BY MORIMOTO AND NAGANO

Part of: Analytic spaces CR manifolds

Published online by Cambridge University Press:  19 December 2019

ALEXANDER ISAEV
ALEXANDER ISAEV*
Affiliation:
Mathematical Sciences Institute, Australian National University, Acton, Canberra, ACT2601, Australia email [email protected]
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Abstract

We consider a family $M_{t}^{3}$, with $t>1$, of real hypersurfaces in a complex affine three-dimensional quadric arising in connection with the classification of homogeneous compact simply connected real-analytic hypersurfaces in $\mathbb{C}^{n}$ due to Morimoto and Nagano. To finalize their classification, one needs to resolve the problem of the Cauchy–Riemann (CR)-embeddability of $M_{t}^{3}$ in $\mathbb{C}^{3}$. In our earlier article, we showed that $M_{t}^{3}$ is CR-embeddable in $\mathbb{C}^{3}$ for all $1<t<\sqrt{(2+\sqrt{2})/3}$. In the present paper, we prove that $M_{t}^{3}$ can be immersed in $\mathbb{C}^{3}$ for every $t>1$ by means of a polynomial map. In addition, one of the immersions that we construct helps simplify the proof of the above CR-embeddability theorem and extend it to the larger parameter range $1<t<\sqrt{5}/2$.

MSC classification

Primary: 32C09: Embedding of real analytic manifolds 32V30: Embeddings of CR manifolds
Type
Article
Information
Nagoya Mathematical Journal , Volume 243 , September 2021 , pp. 209 - 221
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Copyright
© 2019 Foundation Nagoya Mathematical Journal

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Footnotes

*

Alexander Isaev passed away in August 2019. Anticipating that he would not live to see the paper through final revision, he designated Nikolay Kruzhilin at Steklov Mathematical Institute, Moscow, as his proxy. The editorial board thanks Dr Kruzhilin for his kind assistance.

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