On hypersurfaces of S-2 X S-2

摘要

We classify the homogeneous and isoparametric hypersurfaces of S-2 x S-2. In the classification, besides the hypersurfaces S-1 (r) x S-2, r is an element of (0, 1], it appears a family of hypersurfaces with three different constant principal curvatures and zero Gauss-Kronecker curvature. Also we classify the hypersurfaces of S-2 x S-2 with at most two constant principal curvatures and, under certain conditions, with three constant principal curvatures.