Compact Einstein spaces based on quaternionic Kahler manifolds

We investigate the Einstein equation with a positive cosmological constant for (4n + 4)-dimensional metrics on bundles over quaternionic Kahler base manifolds whose fibres are four-dimensional Bianchi IX manifolds. The Einstein equations are reduced to a set of nonlinear ordinary differential equations. We numerically find inhomogeneous compact Einstein spaces with orbifold singularity.