Four-dimensional homogeneous critical metrics for quadratic curvature functionals

TL;DR

This paper classifies all four-dimensional homogeneous metrics that are critical points of certain quadratic curvature functionals, advancing understanding of geometric structures in this specific setting.

Contribution

It provides a complete classification of homogeneous critical metrics for quadratic curvature functionals in four dimensions.

Findings

All such critical metrics are explicitly characterized.

The classification includes known and new geometric structures.

Results contribute to the understanding of curvature functionals in four-dimensional geometry.

Abstract

We determine all homogeneous metrics which are critical for some quadratic curvature functional in dimension four.