Lagrangian submanifolds of constant sectional curvature and their Ribaucour transformation

The Ribaucour transformation is applied to the family of Lagrangian submani folds of dimension n and nonzero constant sectional curvature c of complex space forms of complex dimension n and constant holomorphic sectional curva ture 4c. As a consequence, a process is obtained to generate a new family o f such submanifolds starting from a given one. In particular, explicit para metrizations in terms of elementary functions of examples with arbitrary di mension are curvature are provided. A permutability formula is derived whic h provides a simple algebraic procedure to construct further examples once two Ribaucour transforms of a given submanifold are known. The analytical c ounterparts of the above results are also discussed.