2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74627Chow, Li and Yi in [2] proved that the majority of the unperturbed tori {\it on sub-manifolds} will persist for standard Hamiltonian systems. Motivated by their work, in this paper, we study the persistence and tangent frequencies preservation of lower dimensional invariant tori on smooth sub-manifolds for real analytic, nearly integrable Hamiltonian systems. The surviving tori might be elliptic, hyperbolic, or of mixed type.25 pages. To appear in Nonlinear Analysis: TMADynamical Systems37J40; 70H08text