Compact four-manifolds with pinched self-dual Weyl curvature

TL;DR

This paper investigates compact four-manifolds with harmonic self-dual Weyl curvature under a pinching condition, aiming to classify or understand their geometric structure.

Contribution

It introduces new classification results for four-manifolds with harmonic self-dual Weyl curvature satisfying a specific pinching condition.

Findings

Classification of such four-manifolds under pinching conditions

Identification of geometric structures compatible with harmonic self-dual Weyl curvature

New rigidity results for four-manifolds with these curvature properties

Abstract

We consider compact oriented four-manifolds with harmonic self-dual Weyl curvature in addition to a pinching condition.