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- W4298291219 abstract "We discuss a family $M_t^n$, with $nge 2$, $t>1$, of real hypersurfaces in a complex affine $n$-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 embeddability of $M_t^n$ in ${mathbb C}^n$ for $n=3,7$. We show that $M_t^7$ is not embeddable in ${mathbb C}^7$ for every $t$ and that $M_t^3$ is embeddable in ${mathbb C}^3$ for all $1<t<1+10^{-6}$. As a consequence of our analysis of a map constructed by Ahern and Rudin, we also conjecture that the embeddability of $M_t^3$ takes place for all, $1<t<sqrt{(2+sqrt{2})/3}$." @default.
- W4298291219 created "2022-10-01" @default.
- W4298291219 creator A5025419235 @default.
- W4298291219 date "2013-09-01" @default.
- W4298291219 modified "2023-10-16" @default.
- W4298291219 title "On the Classification of Homogeneous Hypersurfaces in Complex Space" @default.
- W4298291219 doi "https://doi.org/10.48550/arxiv.1309.0279" @default.
- W4298291219 hasPublicationYear "2013" @default.
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