Minimal Lagrangian submanifolds in the complex hyperbolic space

In this paper we construct new examples of minimal Lagrangian submanifolds in the complex hyperbolic space with large symmetry groups, obtaining three 1-parameter families with cohomogeneity one. We characterize them as the only minimal Lagrangian submanifolds in CHn foliated by umbilical hypersurfaces of Lagrangian subspaces RHn of CHn. Several suitable generalizations of the above construction allow us to get new families of minimal Lagrangian submanifolds in CHn from curves in CH 1 and (n − 1)-dimensional minimal Lagrangian submanifolds of the complex space forms CP, CH and C. Similar constructions are made in the complex projective space CPn.