Critical metrics of the total scalar curvature functional on 4-manifolds
A. Barros, B. Leandro, E. Ribeiro Jr

TL;DR
This paper investigates critical points of the total scalar curvature functional on 4-manifolds with constant scalar curvature, proving that under certain conditions, such metrics are isometric to a round sphere.
Contribution
It proves that 4-dimensional CPE metrics with harmonic W+ tensor are necessarily isometric to a round sphere, advancing understanding of the conjecture that all CPE metrics are Einstein.
Findings
4D CPE metrics with harmonic W+ are spherical
Supports the conjecture that CPE metrics are Einstein in specific cases
Provides conditions under which CPE metrics are classified as round spheres
Abstract
The purpose of this paper is to investigate the critical points of the total scalar curvature functional restricted to space of metrics with constant scalar curvature of unitary volume, for simplicity CPE metrics. It was conjectured in 's that every CPE metric must be Einstein. We prove that a -dimensional CPE metric with harmonic tensor must be isometric to a round sphere
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds
