Examples of homogeneous vectors on the fiber space of the associated and the tangent bundles

The paper considers the associated bundle ξ = (G × KG/K, ρ _ξ , G/K, G/K) and the tangent bundle τ _G/K = (T _G/K , π _G/K , G/K, R ^m ), and gives special examples of odd dimensional solvable Lie groups equipped with left invariant Riemannian metric. Some conditions about existence of homogeneous geodesic vectors on the fiber space of ξ and τ _G/K are proved.