Critical metrics on $4$-manifolds with harmonic anti-self dual Weyl tensor

Abstract

We prove that a $4$-dimensional simply connected, compact critical metric of the volume functional with harmonic anti-self dual Weyl tensor and boundary isometric to a standard sphere ${\mathbb{S}}^3$ is isometric to a geodesic ball in a simply connected space form ${\mathbb{R}}^4$, ${\mathbb{H}}^4$ or ${\mathbb{S}}^4.$

Fixed typos

References in corpus (1)

• On the volume functional of compact manifolds with boundary with constant scalar curvature