  We classify real hypersurfaces in complex space forms with constant principal
curvatures and whose Hopf vector field has two nontrivial projections onto the
principal curvature spaces. In complex projective spaces such real
hypersurfaces do not exist. In complex hyperbolic spaces these are
holomorphically congruent to open parts of tubes around the ruled minimal
submanifolds with totally real normal bundle introduced by Berndt and Bruck. In
particular, they are open parts of homogenous ones.
