V. Borrelli, MASLOV CLASS OF A TOTALLY-REAL SUBMANIFOL D, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 323(9), 1996, pp. 1035-1038
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.