Maslov class and minimality in Calabi - Yau manifolds

Generalizing the construction of the Maslov class [µ Λ ] for a La-grangian embedding in a symplectic vector space, we prove that it is possible to give a consistent definition of the class [µ Λ ] for any La-grangian submanifold of a Calabi-Yau manifold. Moreover, extending a result of Morvan in symplectic vector spaces, we prove that [µ Λ ] can be represented by i H ω, where H is the mean curvature vector field of the Lagrangian embedding and ω is the Kaehler form associated to the Calabi-Yau metric. Finally, we conjecture a generalization of the Maslov class for Lagrangian submanifolds of any symplectic manifold, via the mean curvature representation.