  We introduce the notions of strong local Torelli and T-class for polarized
manifolds, and prove that strong local Torelli implies global Torelli theorem
on the Torelli spaces for polarized manifolds in the T-class. We discuss many
new examples of projective manifolds for which such global Torelli theorem
holds. As applications we prove that, in these cases, a canonical completion of
the Torelli space is a bounded pseudoconvex domain in complex Euclidean space,
and show that generic Torelli implies global Torelli on moduli space with
certain level structure.
