2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110341We 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.Differential Geometry53A07; 53A10text