  We prove the existence of a one parameter family of minimal embedded
hypersurfaces in $R^{n+1}$, for $n \geq 3$, which generalize the well known 2
dimensional "Riemann minimal surfaces". The hypersurfaces we obtain are
complete, embedded, simply periodic hypersurfaces which have infinitely many
parallel hyperplanar ends. By opposition with the 2-dimensional case, they are
not foliated by spheres.
