Examples of Minimal G-structures

Let M be an oriented Riemannian manifold and SO(M) its oriented orthonormal frame bundle. Assume there exists a reduction P subset of SO(M) of the structure group SO(dimM) to a subgroup G. We say that a G-structure M is minimal if P is a minimal submanifold of SO(M), where we equip SO(M) in the natural Riemannian metric. We give nontrivial examples of minimal G-structures for G = U(dimM/2) and G = U((dimM -1)/2) x 1 having some special features-locally conformally Kahler and alpha-Kenmotsu manifolds, respectively.