On various types of homogeneous Riemannian spaces with an isotropy group which decomposes

Homogeneous Riemannian spaces are considered whose isotropy group $H$ decomposes into the direct product of irreducible subgroups and the identity operator acting in mutually orthogonal planes in the tangent space of a point $M$. We exclude the special cases when an irreducible subgroup in the decomposition of $H$ is semisimple and acts on a plane whose dimension is a multiple of four. These spaces admit a rigid tensor structuref satisfying the condition $f^3+f=0$.