ON THE CLASSIFICATION OF HOMOGENEOUS HYPERSURFACES IN COMPLEX SPACE

Abstract

We discuss a family [Formula: see text], 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 [Formula: see text] in ℂn for n = 3, 7. We show that [Formula: see text] is not embeddable in ℂ7 for every t and that [Formula: see text] 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 [Formula: see text] takes place for all [Formula: see text].