On the classification by Morimoto and Nagano

Abstract

We consider a family M-t(3), with t > 1, of real hypersurfaces in a complex affine three-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 Cauchy{Riemann (CR)-embeddability of M-t(3) in C-3. In our earlier article, we showed that M-t(3) is CR-embeddable in C-3 for all 1 < t < root(2 + root 2)/3. In the present paper, we prove that M-t(3) can be immersed in C-3 for every t > 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 < root 5/2.