Abstract We study homogeneous Einstein metrics on indecomposable non-Kahler C-spaces, i.e. even-dimensional torus bundles M = G ∕ H with rank > over flag manifolds F K of a compact simple Lie group . Based the theory painted Dynkin diagrams we present classification such spaces. Next focus family l , m n ≔ SU ( + ) × ∈ Z and examine several its geometric properties. show that invariant are not ...