Homogeneous Einstein metrics on non-Kähler C-spaces

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 diagonal beyond certain exceptions their parametrization depends six real parameters. By using an Riemannian metric, compute non-diagonal part Ricci tensor explicitly algebraic system equation. For general positive integers by applying mapping degree provide existence at least one -invariant metric two 2 for obtain four 3 also isometry problem these metrics, while plethora cases induced fixed numerical form all non-isometric metrics.