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ON THE CLASSIFICATION OF HOMOGENEOUS HYPERSURFACES IN COMPLEX SPACE

A. V. ISAEV

Department of Mathematics, The Australian National University, Canberra, ACT 0200, Australia

https://doi.org/10.1142/S0129167X1350064XCited by:2 (Source: Crossref)

Abstract

We discuss a family , with n ≥ 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 ℂⁿ due to Morimoto and Nagano. To finalize their classification, one needs to resolve the problem of the embeddability of in ℂⁿ for n = 3, 7. We show that is not embeddable in ℂ⁷ for every t and that is embeddable in ℂ³ 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 takes place for all .

Keywords:

Global embeddability of CR-manifolds in complex space

AMSC: 32C09, 32V40

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