Pseudo-Riemannian \(T\)-duals of compact Riemannian homogeneous spaces (Q1576597)

The author describes the construction of pseudo-Riemannian homogeneous spaces with special curvature properties, such as Einstein spaces, based on the notion of a certain duality between compact and non-compact homogeneous spaces. A dual pseudo-Riemannian space \((G'/H',g')\) of a compact Riemannian homogeneous space \((G/H,g)\) with homogeneous Spin-structure admits a homogeneous Spin-structure and the \(G\)-invariant Killing spinors on \((G/H,g)\) correspond to \(G'\)-invariant Killing spinors on \((G'/H',g')\).