COMPLETE NONCOMPACT SUBMANIFOLDS OF MANIFOLDS WITH NEGATIVE CURVATURE

In this paper, for an m-dimensional (m >= 5) complete noncompact submanifold M immersed in an n-dimensional (n >= 6) simply connected Riemannian manifold N with negative sectional curvature, under suitable constraints on the squared norm of the second fundamental form of M, the norm of its weighted mean curvature vector | H-f | and the weighted real-valued function f, we can obtain: center dot several one -end theorems for M; center dot two Liouville theorems for harmonic maps from M to complete Riemannian manifolds with nonpositive sectional curvature.