Abstract. We prove the existence of a one parameter family of minimal embedded hypersurfaces in R n+1 , for n ≥ 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.Résumé. Nous prouvons l'existence d'une familleà un paramètre d'hypersurfaces de R n+1 , pour n ≥ 3, qui sont minimales et qui généralisent les surfaces minimales de Riemann. Les hypersurfaces que nous obtenons sont des hypersurfaces complètes, simplement périodiques et qui ont une infinité de bouts hyperplans parallèles. Contrairement au cas des surfaces, i.e. n = 2, ces hypersurfaces ne sont pas fibrées par des hypersphères.
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