Lagrangian submanifolds of Cn with conformal Maslov form and the Whitney sphere

The Lagrangian submanifolds of the complex Euclidean space with conformal Maslov form can be considered as the Lagrangian version of the hypersurfaces of the Euclidean space with constant mean curvature. In this family, we characterize the Whitney sphere as the only compact with null first Betti number and we describe, those compact whose first Betti number is one, in terms of Lagrangian minimal submanifolds of the complex projective space and an one-parameter family of plane curves.