ON the CLASSIFICATION by MORIMOTO and NAGANO

We consider a family, with 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 due to Morimoto and Nagano. To finalize their classification, one needs to resolve the problem of the Cauchy-Riemann (CR)-embeddability of in. In our earlier article, we showed that is CR-embeddable in for all <![CDATA[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 <![CDATA[1<t.