Non-Hopf real hypersurfaces with constant principal curvatures in complex space forms Jose Carlos Diaz-RamosMiguel Dominguez-Vazquez 53C4053C5553C35Hopf hypersurfaceshomogeneous hypersurfacesconstant principal curvatures 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 Br\"uck. In particular, they are open parts of homogenous ones. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4293 10.1512/iumj.2011.60.4293 en Indiana Univ. Math. J. 60 (2011) 859 - 882 state-of-the-art mathematics http://iumj.org/access/