On the classification by Morimoto and Nagano

Alexander Isaev

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arXiv · 1904.05566

On the classification by Morimoto and Nagano

Alexander Isaev

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Abstract

We consider a family $M_t^3$, with $t>1$, of real hypersurfaces in a complex affine $3$-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 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 $1 1$ 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 $1<t<\sqrt{5}/2$.

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Alexander Isaev. 2019-04-11. On the classification by Morimoto and Nagano. https://arxiv.org/abs/1904.05566

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