UNIMODULAR INVARIANTS OF TOTALLY-REAL TORI IN C-N

We investigate invariants of totally real submanifolds in complex spac e with respect to unimodular biholomorphic mappings. This also leads u s to study the invariants of complex-valued analytic differential form s of top degree on a real manifold. The main result of this paper is t o construct a normal form for totally real tori in the complex space u nder the unimodular holomorphic transformations. Some global topologic al properties of noncritical totally real immersions will also be disc ussed.