  Chow, 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.
