On Invariant Sub-Riemannian Structures on Compact Homogeneous Spaces with Discrete Stationary Subgroup

In the paper, invariant distributions on compact homogeneous spaces with discrete stationary subgroup are studied. Special attention is paid to the presence of a sub-Riemannian structure on these distributions and to the condition of complete nonholonomicity. A description of the above homogeneous spaces admitting an invariant completely nonholonomic sub-Riemannian structure is obtained.