2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224997In this paper we will prove that for every integer n>1, there exists a real number H_0<-1 such that every H\in (-\infty,H_0) can be realized as the mean curvature of a embedding of H^{n-1}\times S^1 in the (n+1)-dimensional spaces H^{n+1}. For $n=2$ we explicitly compute the value H_0. For a general value n, we provide function ξ_n defined on (-\infty,-1), which is easy to compute numerically, such that, if ξ_n(H)>-2π, then, H can be realized as the mean curvature of a embedding of H^{n-1}\times S^1 in the (n+1)-dimensional spaces H^{n+1}.14 pages, 8 figuresDifferential Geometry53C42 53C50text