On invariant geometric structures on some compact homogeneous manifolds (Q2719419)

Let \(M=G/H\) be a compact homogeneous space of a connected Lie group \(G\) whose fundamental group is solvable. The paper treats some geometric structures on \(M\) (such as affine, almost-product and unimodular ones) which are invariant with respect to the action of the group \(G\). On each \(M\) of the kind, considered up to finite covering, the structure of a reductive homogeneous space is introduced. Sufficient existence conditions are established for the above mentioned invariant structures on \(M\). Also some counter examples are presented.