Abstract
In this paper, we show that an
n
-dimensional connected non-compact Ricci soliton isometrically immersed in the flat complex space form
, with potential vector field of the Ricci soliton is the characteristic vector field of the real hypersurface is an Einstein manifold. We classify connected Hopf hypersurfaces in the flat complex space form
and also obtain a characterization for the Hopf hypersurfaces in
.