IUMJ

Title: Non-Hopf real hypersurfaces with constant principal curvatures in complex space forms

Authors: Jose Carlos Diaz-Ramos and Miguel Dominguez-Vazquez

Issue: Volume 60 (2011), Issue 3, 859-882

Abstract:

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.