Kähler–Einstein metrics with SU(2) action

Abstract

The aim of this paper is to analyse Riemannian Kähler–Einstein metrics g in real dimension four admitting an isometric action of SU(2) with generically three-dimensional orbits. The Kähler condition means that there is a complex structure I, with respect to which the metric is hermitian, such that the two-form Ωdefined byis closed. It is well-known that if this condition holds then Ω is in fact covariant constant.