New inhomogeneous Einstein metrics on sphere bundles over Einstein–Kähler manifolds

We construct new complete, compact, inhomogeneous Einstein metrics on <f>Sm+2</f> sphere bundles over <f>2n</f>-dimensional Einstein–Kähler spaces <f>K2n</f>, for all <f>n⩾1</f> and all <f>m⩾1</f>. We also obtain complete, compact, inhomogeneous Einstein metrics on warped products of <f>Sm</f> with <f>S2</f> bundles over <f>K2n</f>, for <f>m>1</f>. Additionally, we construct new complete, non-compact Ricci-flat metrics with topologies <f>Sm</f> times <f>R2</f> bundles over <f>K2n</f> that generalise the higher-dimensional Taub-BOLT metrics, and with topologies <f>Sm×R2n+2</f> that generalise the higher-dimensional Taub-NUT metrics, again for <f>m>1</f>. [Copyright &y& Elsevier]