We construct new complete, compact, inhomogeneous Einstein metrics on S^{m+2} sphere bundles over 2n-dimensional Einstein-Kahler spaces K_{2n}, for all n \ge 1 and all m \ge 1. We also obtain complete, compact, inhomogeneous Einstein metrics on warped products of S^m with S^2 bundles over K_{2n}. Additionally, we construct new complete, non-compact Ricci-flat metrics with topologies S^m times R^2 bundles over K_{2n} that generalise the higher-dimensional Taub-BOLT metrics, and with topologies S^m \times R^{2n+2} that generalise the higher-dimensional Taub-NUT metrics.
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机译：对于所有n \ ge 1和所有m \ ge 1，我们在2n维Einstein-Kahler空间K_ {2n}上的S ^ {m + 2}球束上构造新的完整，紧致，不均匀的Einstein度量。 ，在K_ {2n}上具有S ^ 2束的S ^ m的扭曲产品上的紧致，不均匀的爱因斯坦度量。此外，我们构造新的完整非紧实Ricci平坦度量，其拓扑为S ^ m乘以K_ {2n}上的R ^ 2捆绑，以概括高维Taub-BOLT度量，并为拓扑S ^ m \ times R ^ {2n + 2}概括了高维Taub-NUT度量。
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