Curvature properties of Riemannian manifolds with skew-circulant structures

We consider a 4-dimensional Riemannian manifold M endowed with a right skew-circulant tensor structure S, which is an isometry with respect to the metric g and the fourth power of S is minus identity. We determine a class of manifolds (M, g, S), whose curvature tensors are invariant under S. For such manifolds we obtain properties of the Ricci tensor. Also we get expressions of the sectional curvatures of some special 2-planes in a tangent space of (M, g, S).