  We study the global invariants of real analytic manifolds in the complex
space with respect to the group of holomorphic unimodular transformations. We
consider only totally real manifolds which admits a certain fibration over the
circle. We find a complete set of invariants for totally real tori in C^n which
are close to the standard torus. The invariants are obtained by an analogous
classification of complex-valued analytic $n$-forms on the standard torus. We
also study the realization of certain exact complex-valued analytic $n$-forms
on the standard torus through non-critical totally real embeddings.
