MASLOV CLASS OF A TOTALLY-REAL SUBMANIFOL D

On every totally real submanifold M(n) of C-n, we define a closed one form whose cohomology class is the Maslov class of M(n). This form is expressed in terms of the extrinsic local geometric invariants of M(n) and the complex structure of C-n. Then, we define a variational probl em on the space of totally real immersions, whose critical points are totally real submanifolds whose form defined above vanishes identicall y. This extends the well known results on Lagrangian submanifolds of C -n.