Examples of Minimal varvec{G}-structures

Abstract

Let M be an oriented Riemannian manifold and SO(M) its oriented orthonormal frame bundle. Assume there exists a reduction Psubset SO(M) of the structure group SO(dim M) 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 non-trivial examples of minimal G-structures for G=U(dim M/2) and G=U((dim M-1)/2)times 1 having some special features—locally conformally Kähler and alpha -Kenmotsu manifolds, respectively.