On a family of real hypersurfaces in a complex quadric

A. V. Isaev*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)

    Abstract

    We discuss a family Mtn, 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 Mtn in Cn for n = 3, 7. We show that Mt7 does not embed in C7 for every t and observe that Mt3 embeds in C3 for all t sufficiently close to 1. As a consequence of analyzing a map constructed by Ahern and Rudin, we also conjecture that Mt3 embeds in C3 for all 1<t<√(2+√2)/3.

    Original languageEnglish
    Pages (from-to)259-266
    Number of pages8
    JournalDifferential Geometry and its Application
    Volume33
    DOIs
    Publication statusPublished - Mar 2014

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