[en] McDuff proved that the Kaehler form ω on a simply connected complete Kaehler 2n-dimensional manifold P of non-positive curvature is diffeomorphic to the standard symplectic form ω₀ on R²ⁿ. We show that the symplectomorphism she constructed takes a totally geodesic symplectic submanifold Q into a symplectic linear subspace of R²ⁿ. She also proved that if L is a totally geodesic Lagrangian submanifold (P,ω) then P is symplectomorphic to the cotangent bundle T*L with its usual symplectic structure. We extend this result to the case of totally geodesic isotropic submanifolds of P. (author). 8 refs