New Inhomogeneous Einstein Metrics on Sphere Bundles Over Einstein-Kahler Manifolds

TL;DR

This paper introduces new inhomogeneous Einstein metrics on sphere bundles over Einstein-Kahler manifolds, including compact, non-compact, Ricci-flat, and warped product metrics, expanding the landscape of known Einstein geometries.

Contribution

The authors construct a broad class of new inhomogeneous Einstein and Ricci-flat metrics on various sphere and bundle topologies, generalizing known higher-dimensional metrics.

Findings

New compact inhomogeneous Einstein metrics on sphere bundles.

Complete non-compact Ricci-flat metrics generalizing Taub-BOLT and Taub-NUT.

Metrics applicable for all dimensions n ≥ 1 and m ≥ 1.

Abstract

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}, for m>1. 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, again for m>1.