Unimodular invariants of totally real tori in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]

We investigate invariants of totally real submanifolds in complex space with respect to unimodular biholomorphic mappings. This also leads us to study the invariants of complex-valued analytic differential forms of top degree on a real manifold. The main result of this paper is to construct a normal form for totally real tori in the complex space under the unimodular holomorphic transformations. Some global topological properties of noncritical totally real immersions will also be discussed.