New inhomogeneous Einstein metrics on sphere bundles over Einstein-Kahler manifolds

We construct new complete, compact, inhomogeneous Einstein metrics on Sm+2 sphere bundles over 2n-dimensional Einstein-Kahler spaces K2n, for all n>=1 and all m>=1. We also obtain complete, compact, inhomogeneous Einstein metrics on warped products of Sm with S2 bundles over K2n, for m>1. Additionally, we construct new complete, non-compact Ricci-flat metrics with topologies Sm times R2 bundles over K2n that generalise the higher-dimensional Taub-BOLT metrics, and with topologies SmxR2n+2 that generalise the higher-dimensional Taub-NUT metrics, again for m>1