Hadamard foliations of H^n

We introduce the notion of an Hadamard foliation as a foliation of Hadamard manifold which all leaves are Hadamard.We prove that a foliation of an Hadamard manifold M of curvature (less than or equals),a^2 with (less than or equals), a norm of the second fundamental form is Hadamard. For M=H^n we construct a canonical embedding of the union of leaf boundaries into the boundary of H^n. This embedding is continuous and it is homeomorphism on any fixed leaf boundary.Some methods of hyperbolic geometry are developed. It is shown that a ray in H^n with the bounded by (kappa)(less than)1 curvature has a limit on the boundary.