  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 cohomegeneity one. We characterize them as the only
minimal Lagrangian submanifolds in CH^n foliated by umbilical hypersurfaces of
Lagrangian subspaces RH^n of CH^n. Several suitable generalizations of the
above construction allow us to get new families of minimal Lagrangian
submanifolds in CH^n from curves in CH^1 and (n-1)-dimensional minimal
Lagrangian submanifolds of the complex space forms CP^n-1, CH^n-1 and C^n-1.
Similar constructions are made in the complex projective space.
