On higher order Codazzi tensors on complete Riemannian manifolds

The present paper is devoted to the study of the global differential geometry of higher order Codazzi tensors on complete Riemannian manifolds and represents the applications of our results to the theory of locally conformally flat Riemannian manifold and minimal hyper-surfaces in Euclidian spaces. These results will be obtained using theorems on the connections between the geometry of a complete smooth manifold and the global behavior of its subhar-monic functions.