Self-dual Einstein spaces, heavenly metrics, and twistors

Toric Self-dual Einstein Metrics as Quotients

We use the quaternion Kähler reduction technique to study old and new selfdual Einstein metrics of negative scalar curvature with at least a two-dimensional isometry group, and relate the quotient construction to the hyperbolic eigenfunction Ansatz. We focus in particular on the (semi-)quaternion Kähler quotients of (semi-)quaternion Kähler hyperboloids, analysing the completeness and topology,...

New Examples of Einstein Self-dual Metrics

Toric Anti-self-dual Einstein Metrics via Complex Geometry

Using the twistor correspondence, we give a classification of toric anti-self-dual Einstein metrics: each such metric is essentially determined by an odd holomorphic function. This explains how the Einstein metrics fit into the classification of general toric anti-self-dual metrics given in an earlier paper [7]. The results complement the work of Calderbank–Pedersen [6], who describe where the ...

Moduli spaces of Einstein metrics

We discuss the space of Einstein metrics, up to diffeomorphism, on a compact manifold. In particular we mention some heuristics on its dimension and some theorems on its compactness.

A New Construction of Einstein Self-dual Metrics

We give a new construction of Ricci-flat self-dual metrics which is a natural extension of the Gibbons–Hawking ansatz. We also give characterisations of both these constructions, and explain how they come from harmonic morphisms.