On the Schouten tensor of some special Riemannian manifolds

The purpose of this paper is to study some properties of the Schouten tensor arising from the considerations of conformal geometry. In the special cases when the Schouten tensor is recurrent, generalized recurrent and generalized 2-recurrent, it is found the conditions over the manifold. Additionally, in a Riemannian manifold with the constant curvature, it is proved that the Schouten tensor is an Einstein tensor. In the last section of this paper, an example is given for the existence of the Schouten tensor for a 4-dimensional Riemannian manifold.