On weakly Einstein Kähler surfaces

Abstract

Riemannian four-manifolds in which the triple contraction of the curvature tensor against itself yields a functional multiple of the metric are called weakly Einstein. We focus on weakly Einstein Kähler surfaces. We provide several conditions characterizing those Kähler surfaces which are weakly Einstein, classify weakly Einstein Kähler surfaces having some specific additional properties, and construct new examples.

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