On weakly Einstein K\"ahler surfaces

TL;DR

This paper studies weakly Einstein K"ahler surfaces, providing characterizations, classifications under certain conditions, and constructing new examples to deepen understanding of their geometric properties.

Contribution

It offers new characterizations, classifications, and explicit examples of weakly Einstein K"ahler surfaces, advancing the understanding of their geometric structure.

Findings

Characterization conditions for weakly Einstein K"ahler surfaces

Classification results for surfaces with additional properties

Construction of new examples of weakly Einstein K"ahler 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 K\"ahler surfaces. We provide several conditions characterizing those K\"ahler surfaces which are weakly Einstein, classify weakly Einstein K\"ahler surfaces having some specific additional properties, and construct new examples.