  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).
